You are focusing on the too-narrow issue of the new mass, as being only a change of rite.  The issue with new-catholics are the V2 ideals they hold either explicitly or implicitly, consciously or unconsciously, fully or partially.  These false ideals (i.e. the heresies of Modernism in V2...AND the heresies promoted in the 50 years since) they will gradually absorb from the V2 priests, who had V2 seminary training, and from the V2 philosophies of many other liberal/progressive "catholics" who write books, speak, etc and who are promoted by such priests, or at least condoned by their silence.  Those poor novus ordo/indult catholics "don't know what they don't know" and they are being corrupted SYSTEMATICALLY, in schools, in seminaries, in books, in speeches, in false-translations of encyclicals, etc.  All of this happens outside of the 1.5 hrs on sunday at mass.  So even if they go to a "conservative" priest who says a "conservative" novus ordo, their faith is being consistently, systematically and slowly attacked every day of the week by numerous wolves who hide in sheep's clothing.  The problem is much larger than the new rite.

What I had in mind of a Catholic who holds the full faith but attends NO would be one who grew up, was catechised before the V2 reforms and then just continued going to Mass without questioning it after V2 - because well, why would they assume the Church had suddenly flown off the rails? Such a person could be completely unaffected by V2 novelties. Furthermore, there are tons of conservative NOs who were born after V2 who reject ecuмenism and BOD, whereas even Trad founders and leaders such as +ABL embraced BOD. So to frame it as "Everyone in the NO must be at least a material heretic and all/most Trads are not" isn't really accurate. While on Cathinfo most people seem to reject BOD, the SSPX do and have always accepted it(and that's in the modern "other religions can be saved" form, not the old catechumen form) and they're probably the biggest chunk of Trads. 

Most of the heresies that modern "Catholics" embrace aren't even teachings of the Conciliar Church(although they can still be blamed for their spread).

What I had in mind of a Catholic who holds the full faith but attends NO would be one who grew up, was catechised before the V2 reforms and then just continued going to Mass without questioning it after V2 - because well, why would they assume the Church had suddenly flown off the rails?

Firstly, that generation is mostly dead.  Secondly, i've talked to many in that generation and everyone knew that V2 was a change.  The new mass was such a stark, quick and violent rupture with the past that it shocked everyone.  No one could hide from the changes.  You either accepted them through "obedience" (knowing the changes weren't right), you accepted them because you were a liberal at heart who wanted an "easy" Church, or you walked away from the changes and became a Trad.

Such a person could be completely unaffected by V2 novelties.

The only people who didn't realize that V2 was different, were those who didn't know their faith beforehand.

Furthermore, there are tons of conservative NOs who were born after V2 who reject ecuмenism and BOD,

There are many more heresies of V2 than ecuмenism and BOD.  How about "religious liberty"?  How about no salvation outside of the Church (this is separate from BOD)?  Then there's the moral issues which have/will damn many others, even if they reject ecuмenism and BOD - NFP, false-annullments, gαy civil unions, voting for pro-choice candidates, condoning family members who apostasize and become pagan or protestant, accepting sex-ed in schools, accepting euthanasia, etc, etc.  All of these "social issues" are promoted by the local archdiocese.  Even if one attends an indult mass, you are exposed to these dangers to your faith, these temptations to sin, these temptations to compromise.  These dangers are not inconsequential.

First paragraph: I'm assuming he means the group who accepted the changes not because they were liberals at heart, but because of obedience.

Right, but he was minimizing the changes and arguing that those who lived during the 60s and 70s didn't think the changes were "that bad".  That's revisionist history.  Anyone who had an 8th grade understanding of the Faith knew that the new mass was more than just "different".  It was a revolutionary and shocking thing.  Those that quieted their consciences by claiming blind obedience knew that the changes were wrong.

What does "condoning family members who apostasize" mean exactly?

The false idea that a person who stops going to church or switches to protestantism is to be "accepted as they are" because "who are (their family members) to judge".  How many families today accept the errors of other family members by their silence or do so for human respect?  The same heretical mindset is promoted by V2 that any sincere person can be saved in any religion.

Do you believe Lefebvre rejected no salvation outside the Church?

Of course he didn't reject it.  But his understanding of BOD was not 100% orthodox, so his understanding of "no salvation" was faulty.  (By the way, this is why BOD was promoted to begin with by the Modernists in the 30s - to water down the "no salvation" doctrine, so they could usher in V2's new ecclesiology, to pave the way for their hoped-for, freemasonic 'one world religion').  The problem with BOD is that saints do mention it, but the Church has never defined it.  So having a faulty BOD belief is not the same as having a faulty faith due to the indult (in case that's where you were going with this).  Every V2 error has been soundly, clearly and absolutely rejected by a dogmatic statement in the past.  Not so with BOD - there's much misunderstanding and gray area.

Right, but he was minimizing the changes and arguing that those who lived during the 60s and 70s didn't think the changes were "that bad".  That's revisionist history.  Anyone who had an 8th grade understanding of the Faith knew that the new mass was more than just "different".  It was a revolutionary and shocking thing.  Those that quieted their consciences by claiming blind obedience knew that the changes were wrong.

Right, but even if they were wrong, the question still remains of in what way they're wrong. ie. do you consider them no longer Catholic, or merely in error and endangering their faith.  That seems to be what the OP is about, you seem to be saying the former and Matthew seems to be saying the latter.

The false idea that a person who stops going to church or switches to protestantism is to be "accepted as they are" because "who are (their family members) to judge".  How many families today accept the errors of other family members by their silence or do so for human respect?

 For my own part, I am a new convert (as I've mentioned.)  If I have kids some day and one them went Protestant, I would certainly make clear to them that I disapprove, that I seriously fear for their soul, and I would inform them that I intend to pray for their conversion.  So I definitely wouldn't just "accept it."  Would you go further than that, or is that about the same as you would do?  Would you refuse to have anything to do with them?

The same heretical mindset is promoted by V2 that any sincere person can be saved in any religion.Of course he didn't reject it.  But his understanding of BOD was not 100% orthodox, so his understanding of "no salvation" was faulty.  (By the way, this is why BOD was promoted to begin with by the Modernists in the 30s - to water down the "no salvation" doctrine, so they could usher in V2's new ecclesiology, to pave the way for their hoped-for, freemasonic 'one world religion').  The problem with BOD is that saints do mention it, but the Church has never defined it.  So having a faulty BOD belief is not the same as having a faulty faith due to the indult (in case that's where you were going with this).  Every V2 error has been soundly, clearly and absolutely rejected by a dogmatic statement in the past.  Not so with BOD - there's much misunderstanding and gray area.

To be honest, I'm not going much of anywhere in particular.  As I've mentioned, I'm a new convert, and I'm mostly here to learn.  I might state tentative opinions in the pursuit/interest of that end, but I'm not trying to prove myself right, or anyone else wrong, on this forum.  My goal here is primarily to ask questions, listen, and learn.

1: The reason I asked about Lefebvre is because he clearly saw the notion of "Outside the Church there is no salvation" as compatible with the notion that someone could visibly belong to a false religion and still be "inside the Church" somehow.  Your position seems to be that Lefebvre was wrong to say this, but that his erroneously saying so does not constitute either a denial of the dogma or sufficient to make him a heretic.  Given that that's the case, I'm not seeing why you wouldn't give the same charitable assessment to those in the indult who believe basically the same thing.  To be clear, I'm not saying there isn't a good reason, I'm just saying I don't understand what that reason would be.

2: Does even Vatican II say a sincere person can be saved in any religion?  I remember hearing Bishop Barron's whole interview with Shapiro when he said Vatican II says an atheist of good will can be saved according to Lumen Gentium.  And my initial reaction was "I have concerns about Lumen Gentium, but I don't think it says that."  And then I looked Lumen Gentium up, and sure enough, it doesn't say that.  I don't think *even* Vatican II says that someone can be saved without having any supernatural faith at all, furthermore, while Vatican II certainly leaves itself open to the interpretation that someone can in fact be saved while professing a false religion, I don't see how its impossible to read Lumen Gentium as compatible with the notion that if someone with no fault of their own followed the natural law, etc. that God would instead send an angel to such a person rather than leaving them ignorant.  Am I wrong about this?  And if so, why?  (To be clear, I'm not meaning this to be an apology for LG, as it seems to me that the wording was deliberately left very open ended, and that's concerning to me.) 

I just named some examples. EENS is not separate from BOD, as BOD(in its modern incarnation at least - that people of non-Catholic religions can be saved) is the rejection of EENS. Or, at least in our view. The SSPX don't agree with that statement of mine. 

But even if you're right about that, do you have the authority to determine that someone is a heretic because they disagree with you on that?

"I know the Church teaches the immaculate conception, but I just don't believe it."  If someone says that, they just clearly aren't a Catholic.  Like they're straight up denying a dogma.  That's clear.

"I believe that Outside the Church there is no salvation, but I disagree with your interpretation of it, [insert reason here]" seems way less clear, either way.

What I had in mind of a Catholic who holds the full faith but attends NO would be one who grew up, was catechised before the V2 reforms and then just continued going to Mass without questioning it after V2 - because well, why would they assume the Church had suddenly flown off the rails? Such a person could be completely unaffected by V2 novelties. Furthermore, there are tons of conservative NOs who were born after V2 who reject ecuмenism and BOD, whereas even Trad founders and leaders such as +ABL embraced BOD. So to frame it as "Everyone in the NO must be at least a material heretic and all/most Trads are not" isn't really accurate. While on Cathinfo most people seem to reject BOD, the SSPX do and have always accepted it(and that's in the modern "other religions can be saved" form, not the old catechumen form) and they're probably the biggest chunk of Trads.

Most of the heresies that modern "Catholics" embrace aren't even teachings of the Conciliar Church(although they can still be blamed for their spread).

My parents fall into the first category, one that is quickly dying out.  Remember, Vat. 2 finished in 1965.  There are many still living who were young adults, teens, or children at that time, or who came of catechism age under John XXIII up through the early 70s.  IOW, too young to know, or devout, but poorly catchised.  My folks are in their 90's and still attend the novus ordo, health permitting. They were both poorly educated on Catholic dogma and know very little of Church history, no fault of their own.  They were raised, like nearly all Catholics of their day, to be obedient to authority, especially Church authority, agree or not!  They learned their prayers, and the catechism by rote, not meaning.  They were tested for the Sacraments by rote recitation of the catechism.  
Those who came later weren't taught dogma, either.  They threw out the old catechisms, threw out the rote, and were taught touchy-feely pablum and communist social justice.  The sheep were first set up to accept lies, and the lies were fed to their off-spring.  My parents won't attend the Old Mass, even though I think they want to, because they asked "Fr. Mike" about it and he said it was a mortal sin!  The only place they could go, although he didn't recommend it, was to the diocesan approved Indult, a 60 mile drive one way.  That was ten years ago when I began making biweekly drives through two states to hear Mass.  Prior to this, I'd tried out various Protestant churches, went to the novus ordo after reading Jurgen's Lives of the Saints---all of it, the original edition.  After a short time, I saw that Vat. 2 had all but destroyed the true  faith, and that I'd been gypped out of my religion.  It resulted in arguments that always ended up with the good fruit the Catholic practices with which my parents raised us, still practice themselves, even my siblings do not.  Despite them attending the new mass, I have no doubt they have the Faith.  Their parish is still conservative enough, Fr. Mike, notwithstanding, that Rosaries are seen among the older folks, and one can receive communion on the tongue, if desired.  They always go to the priest's line, not the aging hippie lady eucharistic minister.  They just lack the grace of understanding.  There's a built in resistance to studying dogma and scripture without the direct guidance of a qualified religious.  They say it's a result of my foray into Protestantism, that it's not Catholic.  And under normal circuмstances, they're right. 
Still, for anyone to ascertain my parents are bound for hell is extremely presumptuous.  Not one of us knows for sure where even we ourselves will go, much less the souls of persons unknown to us.  

With regard to the core dogmas, there are more Feeneyites within the Novus Ordo than among Traditional Catholics.  What other error would disqualify them from being Catholics?

Honestly, I don't get this, but given that that's the case, I don't know how to agree with the strict "the Novus Ordo is a different religion" approach rather than the more modest "Vatican II is ambiguous enough that its very easy to read in a heterodox way.

Are there any explicit dogmas on religious liberty?  Even if they are, would getting that wrong disqualify one from being Catholic?  (even if Pius IX's Syllabus of Errors was infallible, couldn't someone think it wasn't?  Or couldn't someone propose a way to reconcile DH and Syllabus of Errors?  Even if doing so was silly, would it make them not Catholic?)

Do you take the position that only Feeneyites are Catholic? 

Anyone in their late 70s and older was probably catechised before V2 was finished, or before V2 reforms were put in place. And most NO masses are mostly the elderly these days, so it's quite a large proportion of people who still attend Mass regularly. The toning down and declawing of catechising in schools was a very gradual process too, my father who went to school after V2 was still catechised well in school and told all the "non-PC" things they'd be afraid to teach today(e.g EENS). So my grandparents had no reason to be concerned with what the Brothers were teaching him, and even in a scenario where the teaching had been toned down, most people would put that down to modernists refusing to teach properly rather than the Church actually abandoning its dogmas. 

The issue of changes to schooling is separate from the changes to the Mass.  The new mass came first, and was the priority.  All else came after the new mass was already accepted.  If you were corrupted by the new mass, your Faith was already damaged (and for many, on life support), even if your schooling was mostly "normal".

And people were shocked by the changes to the Mass, but the Church had decreed what the Church had decreed. For most people it was out of question to just stop going to Mass, and they'd be afraid of committing schism by attending societies such as the SSPX if they had even heard of them. For example, Tolkein famously continued to shout out Latin responses in Mass, so he was very upset with the new rite. But he kept attending the NO despite clearly preferring the old rite, and I believe it's for the reasons I listed. 

Traditionalism started day 1 after Vatican 2.  Many catholics of this generation left new-rome and many priests did as well, in order to preserve Tradition.  Your description above is revisionist history.  What Tolkien did, in his particular country, is of no consequence to what 1,000s of Catholics did in America to keep the Faith.

Why would someone stop attending their local parish Mass because some other diocese had some pro-gαy event or whatever? What does that have to do with the Mass?

Traditionalism is about MORE than the mass.  Keeping the Faith is more important than the mass.  A catholic cannot attend his indult mass, where Fr X says a reverent liturgy, and ignore the fact that 2 hours later, Fr Y comes in and dances around (ON THE SAME ALTAR) and makes jokes and hands out wine and cookies.  Or worse, Fr X says both the indult AND the new mass, which is the height of hypocrisy.  This type of action is inconsistent with catholicism - you cannot accept evil to get good.  The end (having a reverent liturgy) does not justify the means (accepting the abominable new mass as the "ordinary" form).