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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).