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".
I do believe they're mistaken, but that's a separate issue from your question.
One of the mistakes made by the dogmatic Dimondite crowd is in fact to equate BoD with EENS. I think the greater dogma that's being rejected is Trent's teaching that the Sacrament of Baptism is necessary for salvation. Most promoters of BoD articulate their position in such a way as to contradict that dogma, and also slide into Pelagianism.
Now, those who veer off into claiming that infidels can be saved, those do in fact not believe in EENS. They think they do, but their positions clearly reject Catholic dogma. I doubt many of them are guilty of pertinacious heresy, but they have been confused and befuddled by their teachers, and believe that they are in fact following Catholic teaching.