The sspx follows a kinda-probablist opinion on the new rite.  Their reasoning is flawed.  We cannot presume validity for rites (i.e. V2 rites) which aren't officially promulgated by the Church.  We MUST choose certain rites (i.e. Traditional).  Allowing, condoning or conferring "probably valid" rites is condemned and prohibited.

“We cannot choose a less certain option, called by the moral theologians a simply probable manner of acting, that could place in doubt the validity of the sacraments, as we are sometimes obliged to do in other moral questions. If we were able to follow a less certain way of acting, we would run the risk of grave sacrilege and uncertainty concerning the sacraments, which would place the eternal salvation of souls in great jeopardy. Even the lax “probabilist” theologians admitted this principle with respect to baptism and holy orders, since the contrary opinion was condemned by Pope Innocent XI in 1679.

It is permissible in conferring sacraments to follow a probable opinion regarding the value of the sacrament, the safer opinion being abandoned.... Therefore, one should not make use of probable opinions only in conferring baptism, sacerdotal or episcopal orders."
--(Proposition 1 condemned and prohibited by Innocent XI, Dz. 1151)

Consequently, it is forbidden to accept a likely or probably valid ordination for the subsequent conferring of sacraments. One must have the greatest possible moral certitude, as in other things necessary for eternal salvation. The faithful themselves understand this principle, and it really is a part of the “sensus Ecclesiae,” the spirit of the Church. They do not want to share modernist, liberal rites, and have an aversion to receiving the sacraments from priests ordained in such rites, for they cannot tolerate a doubt in such matters. It is for this reason that they turn to the superiors to guarantee validity.”


-- Fr Scott, sspx, 2007
https://sspx.org/en/must-priests-who-come-tradition-be-re-ordained-30479

It seems you "usually" follow the judgements of the SSPX. I would guess you choose to do so, because of the trust you place in their founder and the good fruit that has come from their Apostolate? I appreciate you taking the time to respond.
As for your answer to number 2 - one thing does not automatically follow the other, "If the priest is traditionally ordained, his baptism was valid.".

By "usually" I mean that I take the orthodoxy of the priest into consideration. But again for me, I have not needed to worry about this issue for decades because when we get new priests, they keep sending their own priests, priests who were ordained by the SSPX. Fr. Horvath was one conditionally ordained that I met in Louisville, KY about the year 2006 or 2007 I think, then some 6 or 7 years later he administered the Last Rites to me before my surgery. I did not ask him if he was conditionally baptized, they will not conditionally / ordain anyone who has a doubtful baptism.

I heard that Fr. Robinson was in charge of looking into these things now (from the side of N.O. priests coming over to Tradition), is that true?

I don't know, what I do know is they already know there are certain NO bishops that they do not trust to ordain validly, so those priests get very little or no investigation.

You can say the new rite in Latin, or French, or greek...it doesn't change the fact that this rite is positively doubtful.  Fr Hesse's arguments are based on probabilities and guesses.  He was a doubtful priest, period.

Agreed.  So in the NO Rite (Latin vs. English is irreelvant), they removed the "ut" ... from the essential form AND all the surrounding references to a specifically-Catholic notion of the priesthood, and Pope Leo XIII stated that the Anglican Orders were invalid even after they had corrected the essential form due to the surrounding stuff.

So, people say, eh, it's just a two-letter word.  How could it possibly affect validity?  OK, well, if it's JUST a two-letter word, so why did they feel a need to remove it?  Did it make that much of a difference to making the meaning oh-so-much-more modernized and relevant to "modern man"?  That speaks to some malicious intent there, as there's no good reason it had to be removed ... other than if you're looking to deliberately vitiate and invalidate the essential form.

And here's the problem ... the "ut" means "so that", meaning that what comes after it is known as the Sacramental Effect, and what comes before it is the cause of said Effect.

Pius XII declared that the essential form included an invocation of the Holy Ghost in order to produce the Sacramental Effect that is being named.

So here's the meaning change.

OLD:  May the Holy Ghost come down to make this man a priest.
NEW:  May the Holy Ghost come down.  May this man become a priest.

So in the first form, you're clearly indicating that you're asking the Holy Ghost to turn the man into a priest.

In the second, the new, you're asking for the Holy Ghost to come down.  Then you're asking (God? the Holy Ghost?) that this man might become a priest.  It's not unequivocally and unambiguously clear.  You could argue that it's implied, but I don't think it is necessarily (unless you already know the previous version and are reading that meaning into this).  Taken standalone, without that context of what came before, "unburdened by what came before", as hαɾɾιs would say, I could just be asking the Holy Ghost to come down ... so as to ... give this man graces to become a good priest, various actual graces, or to have the right dispositions to become a good pirest.  If I didn't know anything about the Sacrament and no memory of the previous Rite, I can't say for sure what this prayer is asking the Holy Ghost to do in connection with making the man a priest.

In other words, you're separating the invocation of the Holy Ghost from any explicit connection with the Sacramental Effect.

That's a SERIOUS problem ... whether in Latin or in vernacular.

This would actually be a great Motto for the Conciliar Church:

Ok, so you think that you know better than +ABL, +Fellay, Fr. Franz Schmidberger and +Williamson. Good for you.

It's not about "knowing more"; it's about having as much certainty as possible (as canon law requires, and as Pope Innocent demands).

+ABL's policy changed a few times, and in the beginning might have been ok because there were still old-rite bishops consecrating new-rite priests.  But as time went by, old rite bishops died off, which means the policy had to change.  At the time of his death, in the 90s, the sspx's policy was to conditionally ordain.

+Fellay and Fr Schmidberger are neo-Trads who want a deal with new-rome.  Can't trust their view on the matter.

+Williamson has always been back-n-forth on the new rites (and even the new mass).  His view isn't based on facts, but more on emotion.

I don't have to "know more" than the above people; I just have to apply principles, follow canon law and follow what Pope Innocent said.  It's not that complicated.

It seems you "usually" follow the judgements of the SSPX. I would guess you choose to do so, because of the trust you place in their founder and the good fruit that has come from their Apostolate? I appreciate you taking the time to respond.

As for your answer to number 2 - one thing does not automatically follow the other, "If the priest is traditionally ordained, his baptism was valid.".

I heard that Fr. Robinson was in charge of looking into these things now (from the side of N.O. priests coming over to Tradition), is that true?

Which Fr. Robinson?  The good one, I hope.

+ABL and the others, including Fr. Hesse himself, said that the validity of his ordination was without doubt. Yet here's you saying they were all wrong, "period." 

Well, apart from the fact that I've only ever seen this claim made by Fr. Hesse himself, who, even if not outright lying, may have been applying some spin, and he definitely likes to spin tall tales (reminding me a bit of Malachin Martin), but ... if they said these things ... then, yep, they're wrong.

Now here's where you can come out from hiding behind your selective argument from authority ... we explained why they're wrong.  You're welcome to refute it.  That's how actual arguments work, not by flinging around ridiculous fallacies.

You said "in the beginning might have been ok because there were still old-rite bishops consecrating new-rite priests." So first, by your own admission that shoots your statement about Fr. Hesse in the foot.

I was paraphrasing +ABL's argument.  I don't agree with it.

Second, if all it took was an old rite bishop, then the new rite in and of itself is valid, if it is valid, then so are all the NO priests and bishops ordained /consecrated in the new rite since they all can trace their lineage back to old rite bishops. But there is more to it than that.

Yes, this is the logic of +ABL and the "classic" sspx.  Which is, obviously, flawed.  I think it's totally wrong.  As you admit "there's more to it than that".  And there is. 

Even +Tissier says that the new rites have 'positive doubt'.  And +Tissier's analysis agrees with many other Trad clerics (i.e. it's the "consensus" if such a thing exists).  Therefore, this is why I said that ... "Fr Hesse is doubtful. Period."  Because I go based on facts, which is what +Tissier bases his opinion on.

The other problem with the new rites is admitted by Fr Hesse, when he said his ordination was done "by the book".  This implies that many are not.  And if one isn't paying absolute attention the entire (multiple hours) ceremony, then 'modernist' things can slip in.  No amount of investigation can lift this type of doubt.  Because you can't go back in time and witness the ceremony.  Therefore, there's doubt.