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So ... I do not consider semi-trads to be the same as being adherents to a "false religion", not formally, because they haven't been condemned by papal authority, but only based on our judgment.  It's not the same as being a member of the Orthodox Church.  There are some in the Conciliar Church who err in good faith, and that's probably true of most if not all the semi-trads, as you refer to them.  I in fact call them "trads", vs. "Trads" (capital T) for actual Traditionalists.

Now, "sympathy" for (an actual) false religion is not intrinsically mortal sin ... but if it's somehow a temptation for you that might lead to religious indifferentism, it could be mortal sin if you indulge in it knowing it to be a near occasion of sin for you, where it causes you temptations against the faith.  CHRONICALLY indulging in such emotions can weaken your faith.

You're better off "emoting" for the PEOPLE in the false religious, and in particular out of sympathy for them rooted in a desire for their conversion, at which point it's not only not a sin but can even be a virtue.

So, this problem does arise in general where people's feelings of sympathy for (those in) false religions, on a NATURAL level, leads to an erosion of SUPERNATURAL faith, and as long as we keep the two very clearly distinct in our minds, it's perfectly fine to have natural sympathies, to feel sorry for people, etc. -- but we don't do violence to Church dogma regarding salvation simply because we sympathize with them and feel sorry for them.

This reminds me of (note: I’m not saying it’s the same as… just that it happens to remind me) someone here back when I was still Catholic telling me I was not really Catholic because I admitted I was not absolutely certain the Orthodox Church was not true, I was only certain that Protestantism is not true.  I understand this is a tangentially related question to OP, but… how does this not destroy the visiblity of the church, if someone who is visibly a member of the church is actualy not a member of the church due to possessing doubt?  I understand that you could say the visibility of the church is damaged because of Vatican ii or the fact that an antipope is in Rome or something like that.  But I kind of just intuitively doubt (and I admit I can’t prove this) that all or even nearly all pre Vatican ii bishops consistently formally excommunicated anyone who had any degree of doubt about any dogma, maybe someone who obstinately denied it or publicly went around denying it, but not merely a person who simply wasn’t as certain as they should be about it.  Basically I’m hinting at the opposite problem to the one you’ve often mentioned (and I see your point) about “non feeenyite” ecclesiology logically leading to Vatican ii and a sort of franken church that only subsists in the Catholic Church, but also include includes non-catholic.  Saying that people who are visibly and publicly identified in the Catholic Church are “not Catholics” because of some interior doubt or disposition seems to logically be the other side of the same coin.  Thoughts?

I dont' believe St. Robert would have used the term soul, as many later believed that he was so insistent upon Church as visible society that it was almost to a fault.

He actully limited the possibility of BoD to catechumens, since they were at least to some extent visibly united to the Church, and he described them as being "in the vestibule of the Church".

While at another he taught that members needed to meet ALL FOUR criteria for membership, it almost sounded as if he implicitly held some notion of a partial membership sufficing for salvation, i.e. where even if you weren't united to the Church in the Sacraments, you still professed the truth faith.

So doubt precludes the profession of faith, and profession of faith, or, rather, faith itself, requires absolute certainty.  There cannot be supernatural faith that admits of any doubt.  I may have been the one to tell you that if you're not sure about Catholic vs. Orthodox that you do not have the faith and are already outside the Church.

So, the visibility of the Church consists of four criteria:  1) visible / physical membership via the Sacraments, 2) outward professoin of the true faith, 3) public professoin of submission to he Supreme Pontiff, and 4) non-excommunication.  If any of those is missing, there's no membership in the Church.  In doubting about 2 vs. 3, you were failing criteria 2 & 3.

Now, pre-V2 bishops would not excommunicate those who had any doubt about dogma, especially if these doubts were of the private variety.  If they were in PUBLIC doubt, and/or could potentially be influential, where some individual were doing harm to souls ... that might have warranted excommunication, but that was rarely teh case.  When people doubted the Church, it just took care of itself, where they left.

I have more questions if you don’t mind

first of all, maybe this isn’t a real objection, but I just seriously doubt that the vast majority of Catholics at any time of history after the intention of the printing press at least “never had any doubt” about the correctness of their position.  This sorta raises even weirder questions about process as well.  So say one day a Catholic starts doubting something, like not necessarily on purpose but like the question of “what if X is false”pops into their head and they struggle with that for a day or so, do they have to be readmitred into the church after that resolves?

more importantly, to me your last paragraph seems to contradict the rest of your argument.  If these people are indeed “not Catholic” shouldn’t they be excommunicated? I mean, I get that this is impossible if the doubt is literally admitted to nobody, but do you think the majority practice at any time, say, if someone admitted to doubting in the confessional, or the bishop was aware that they doubted, that there would’ve been an excommunication?  And if not, why not?