To reject that the teaching magisterium is the rule of faith is a heresy.

No.  What I am saying is that a Catholic who innocently hold a heresy does NOT reject the teaching magisterium as the "rule" of faith.  He only errs innocently regarding what the magisterium actually teaches on the matter in question. 

Here is a good article on the matter:

https://wmreview.co.uk/2023/01/23/objection-ii/

No.  Cf. Bishop Sanborn, Fr. Cekada, and others who state that it's fine to use the titles by which people are commonly known and that it's not tantamount to an affirmation that there's no doubt about Holy Orders.  On top of that, since I don't hold that they're certainly invalid, he deserves the benefit of doubt in terms of respect, even though I would not receive Sacraments from him unless I had no other option in danger of death, per Canon Law.

God bless you, Lad - I appreciate your opinion and reply. Good to know you would avoid receiving Sacraments from him. That you don't believe they're certainly invalid is another way of saying there exists a positive doubt - which as Catholics we are under obligation to avoid ...and my main point. However, as is the case with other issues, I disagree with + Sanborn's and Fr. Cekada's (R.I.P) opinion. When it comes to the Sacraments, respect doesn't enter into the equation.

And then there is a third type whom were not mentioned:  There are those who say, "I do not know if Francis is pope, God knows, and frankly I could care less about the matter.  Do not attend the heretical New Mass, go to the traditional sacraments, say your rosary, and carry on soldier."  Yes indeed, we do meet all kinds.

Catholic Knight ... your last post was correct.

Formal / Material has nothing to do with "innocence", "sincerity", etc. where it comes to dogmatic theology, but has a place only in moral theology with regard to the internal forum, where sin or moral fault may be exculpated by an invincible ignorance.

With regard to Catholic faith, the material aspect has to do with WHAT is believed, and the formal with WHY it's believed.

I could sit down, read my Bible, apply my own private interpretation, and come up with a set of beliefs that is 100% consistent with Catholic dogmatic teaching.  But I'd still be a formal heretic, since I do not adhere to those beliefs due to an infallble God-given rule of faith.  I believe all the WHAT but not due to the correct WHY, i.e. I would lack the formal motive of faith.

I am a Protestant, and with total innocence and sincerity believe my religion to be true.  Yet this sincerity matters nothing.  While God would not impute moral guilt to such a one, despite his innocence, he lacks the formal motive of faith, submission to the Church's Magisterium as the rule of faith, and therefore despite all the sincerity in the world, he's a formal heretic.

I am a Catholic who adheres to one or another heresy, but it's only because I'm a poor uneducated peasant and a dummy with low IQ (Johannes here can relate).  I know about the Church and have every intention to believe everything the Church teaches (as expressed, say, in the Act of Faith).  I am a Material heretic only.  St. Augustine lays down the litmus test for this type of heretic as being someone who would immediately abandon his former heretical belief once informed of the truth.  I recall when I was young that I had a heretical view of the Immaculate Conception.  But as soon as someone told me, "Uh, well, that's not what it means.  This is what the Church teaches about it.", my response was, "Oh, sorry." and I instantly adhered to this correct belief.  That's material heresy, and that alone is material heresy.  Now, in this case, there could be SOME culpability that God would imput to me as sin, i.e. if I were too lazy to study my catechism, that might be a mortal sin to adhere to such heresy, but we're back now into the internal forum, whic God alone can discern.

Now, I claim to be a Catholic but I decided that, despite the Church's teaching, I don't believe in papal infallibility.  It's total bunk, perhaps even heresy.  I'm a formal heretic.  That's because, knowing what the Church teaches, I reject it anyway, and basically reject the infallible teaching authority of the Church as my rule of faith, but prefer my own private judgment.  This is why they say that if you deny one dogma you deny them all, because in denying the one, you deny the rule that underlies all dogmas, thereby showing I don't have the formal motive of believe, even if I happen to believe ever single dogma besides that one, since I now believe it because I choose to believe it, following my own lights as my rule of faith.

So ... this notion of formal vs. material heresy somehow pertaining to sincerity and the internal forum has been a gradual butchering of the terms with a view toward undermining EENS dogma.

There are in fact many in the Novus Ordo who think the Conciliar Church is the Catholic Church because they see this guy calling himself pope and prancing around Rome in a white cassock.  They may or may not even know what's in Vatican II, much less believe what's in it.  And if they do believe it, if their motive is, "Well, the Church teaches this, so I accept it." ... they have the formal motive of faith and are material heretics only.  I know many such.  Again, I ask myself, if there were a Traditional pope elected and the Church restored, if the pope then condemned, say, Religious Liberty, would this person accept it.  In many cases, I'm sure that he would.  And, in either case, I can't judge them to be outside the Church by assuming that they would not.

I would love to hear how they met?  Was he conditionally consecrated? What was going though +Vigano’s mind about +Williamson etc…

Take Athanasius Schneider.  Identity the heresy he professes and adheres to and provide evidence.

+(?)Schneider may be a heretic on EENS.

It is manifest, but I am unsure of this being formal or how culpable he may be.

+(?)Schneider may be a heretic on EENS.

It is manifest, but I am unsure of this being formal or how culpable he may be.

What's the trad position on EENS?