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Very few priests indeed reject Baptism of Desire.

That's not necessarily the equivalent of not believing in EENS.  St. Thomas Aquinas, St. Robert Bellarmine, and St. Alphonsus all clearly believed in EENS, and held to versions of BoD that did not intrinsically undermine EENS.  So I think that it's important to distinguish.

I have in fact met some priests, inside the SSPX, and elsewhere, who believed that explicit Catholic faith is necessary for salvation (at least in the bare minimum as taught by the Church) even though they believed in BoD.  I would not categorize that as "not believing EENS".

It's worth noting that the CMRI won't prevent you from attending chapels or receiving sacraments over "Feeneyism", they just ask you to not proselytize. Even the Dimonds concede this and I personally have received some degree of confirmation to this. Matthew has a good view on this that holds some truth - that "Feeneyites" are apostles and want to spread their ideas. This is a drama vector. I think the Crawford case in particular has something going on that other people aren't privy to, beyond just those letters etc. I assume something else was happening. Just go to your chapel and don't blackpill and become a home-aloner.

If someone is a catechumen and they die before baptism, to me, this seems like a move of Providence on the part of God, as Calvinistic as it may sound. He ultimately knows who will and will not be saved, yet He wills that all men be saved of their own free will to respond to grace.

I would agree that BoD with explicit faith is understandable and have more room to err in good faith, but how could you be OK with someone who hold a theological position you consider erroneous? Follow that path logically, if not reject EENS, they would either denies the Sacrament of Baptism is absolutely necessary for entrance into the Church, or water is absolutely necessary for the Sacrament. Both of them, in light of the dogmatic definitions, are heresies.

But the (non-Pelagian, non-heretical) BoDers do continue to maintain that the Sacrament is absolutely necessary for salvation.  What they say though is that the Sacrament is necessary in desire.  They say it's necessary to receve in voto even if not necessarily in re.  That's a faulty argument made by many of the Dimondite anti-BoDers  You can still say the Sacrament of Baptism is necessary for salvation even if you allow for the modality of receiving it in voto.  Trent itself teaches that the Sacrament of Confession is necessary to be restored to a state of grace after a post-Baptismal fall, but clearly holds that it can be received in voto.  About Confession Trent says, saltem in voto, "at least in desire".  Since the Church has tolerated this opinion and even made Doctors of the Church a couple of me who held that position, it would be rather presumptuous to hold that the opinion is not at least tenable.  I think it's wrong and mistaken, for reasons I have articulated elsewhere, but I don't hold that it's inherently harmful to the faith if understood as St. Thomas, St. Robert, and St. Alphonsus held it.