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It is a sin for Catholics to hold contrary beliefs to the clear de fide teachings of the Church. The distinction you're seeking is whether holding contrary beliefs is sin of heresy, which we cannot say until that contrary belief is professed, or is it just an error due to being mistaken, in which case is the error corrected when the mistake is realized. Does the mistake become the sin of heresy if the contrary belief is maintained after being corrected? Seems like it to me.

No, you don't make the necessary distinctions here.  Someone could hold a believe contrary to the clear de fide teachings of the Church out of ignorance, in which there's NO SIN AT ALL if it's not a culpable ignorance.  As soon as it becomes a sin, then the rejection of "clear de fide teachings of the Church" is most certainly heresy.  If it's a sin, then it's heresy.  If it's just a "mistake," then there's no sin at all, much less a sin of heresy.

Just for the sake of clarity, the focus here is not on whether or not BoD is an error (I believe it is), but whether those who hold to the theological opinion of such are either obstinate, hell bound heretics (as the Dimonds hold, unless you're a canonized saint); or that they are Catholics in error.

On the basis of Brownson's distinctions, I'm arguing for the latter. Fr. Feeney appears to have been of the latter camp as well.

Again, I have never seen MHFM condemn someone of heresy before they contradict a dogma of the Church.  And apparently they don't condemn you merely for affirming BOD.  They always wait until they have cornered you and gotten you to admit that you make exceptions to the defined dogmas or that you continue to contradict a dogma despite them pointing out that you are contradicting a dogma.  I think they are fair.  And based on the arguments that have erupted here on Cathinfo, I would say that most of the defenders of EENS likewise will condemn you of heresy if you continue to contradict dogmas after being informed of the contradiction.  Maybe MHFM's biggest problem is that they have shown that the vast majority of traditional Catholics contradict one dogma or another.  That makes them very unpopular with trads because no one likes to be humiliated.  But they are having a lot of success with non-trads.

Also, despite the fact that I disagree with them about condemning trads for heresy, I realize that their approach might be the right approach.  I'm not infallible.  Maybe they are correct on that point too.  Personally, I have always looked at these uncertainties with an eye to risk/reward.  What's the risk of taking a certain position and what's the reward?  Sede vacante is easy.  What's the risk of going sede vacante and getting it wrong?  None.  The Novus Ordo popes preach universal salvation, partial communion, etc.  To them the Church is a big tent covering everyone.  What's the risk of going with the Novus Ordo and getting it wrong?  You're outside the Church and you can't be saved.  Easy decision.  But what about taking a hard line on formal heresy and getting it wrong?  Well, given that Our Lord said we will be judged according to the same measure we judge, I would say it is a serious risk.  What about going too easy?  You could become slack in the faith and lose it.  So no easy decision there.  So I'm trying to be cautious.  Don't have too much contact with BOD hard liners but don't condemn them as formal heretics either.  I think they have made an error and I don't want that to rub off on me.  But I don't think it is a good idea to break communion at this point either.  And I think maybe MHFM sees it that way too.  They still receive sacraments from valid priests even if those priests are preaching heresy on EENS.  But they won't hear any sermons or support them in any way.  So is that breaking communion or not?  I don't know.  Trying to figure this all out is a major headache.