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How exactly have you researched their positions?  As a "student of the Church" one would suspect that you have access to approved, pre-conciliar works on various topics they address: baptism, heresy, etc. You've really not ever come across anything in any Catholic material in tension with the Dimond's material?
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Rejecting the salvific quality of baptism of desire is their most glaring error.  They err not just in their rejection but also as Ladislaus pointed out, in their conviction that baptism of desire is heretical.  This means that the whole magisterium has maintained soteriological error for at least four centuries.  For, since Trent at least, baptism of desire has been affirmed by everyone who has taught on the matter.
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I was also surprised, several years ago, to discover that even their case for sedevacantism is a wreck.  Their argument revolves around a lack of supernatural faith on the part of the conciliar claimants, and they argue that this lack constitutes their non-membership.  This is the kind of nonsense one ends up committed to when one develops a disdain for the ordinary magisterium.  It is abundantly clear within the Tridentine tradition, especially since Pope Pius XII's Mystici Corporis Christi (but really since Bellarmine's de Controversiis) that supernatural faith is not a condition of Church membership.  
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Of course they present themselves as just "bringing up dogma and doctrine that has already been settled or proclaimed" but they do it in a very crude, used-car salesman way.  The Catholic faith cannot and is not reducible to a checklist of discrete anathemas; the ordinary magisterium constitutes the bulk of what we know to belong to the Catholic faith: the sainthoods of Ss. Peter, Paul, and more than a thousand years worth of saints; the existence of guardian angels, the efficacy of sacramentals, the perpetual virginity of the Virgin Mary, and so on.  Not to mention that what is solemnly defined is, per Vatican I, to be understood according to the way the Church understands it-- not in a vacuum "as it reads" or whatever other propagandic axioms the Zirconium boys like to circulate.  With the blinders off, it becomes quite evident that they present nothing other than their own spin on things and intellectually bully people into thinking that their understanding is the only true and obvious one.  Of course if that were true, then their whole apostolate would make no sense at all; one hardly needs a teacher or interpreter for what is obvious!

The sort of enlarged, elastic approach to EENS common in the Novus Ordo-- describing the Catholic Church as the "privileged path" like Robert Barron did to the Jєω Ben Shapiro-- is certainly a complete failing and dereliction of duty.  As to the exact limits of baptism of desire, my own personal opinion is that it is doubtful that anyone can be saved without explicit faith in the Trinity and the Incarnation, although an implicit desire for baptism (accompanied by an explicit faith in the Trinity and the Incarnation) would certainly suffice, per Saint Alphonsus.  Perhaps it is the case that an implicit faith in the mysteries would suffice in some instances, though that is far from certain and Tradition seems to weigh rather heavily on explicit faith at least in those two mysteries being necessary for salvation.  
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The Dimonds' reject even this "narrower" view, though.  Yet this is the teaching of the Council of Trent; it isn't merely the teaching of the ordinary magisterium for the last five hundred years (perhaps even longer-- which alone suffices to prove the apostolicity of the doctrine), but it's right there in Trent.  Trent describes the catechumen as being capable of being justified before the sacrament is received.  
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The sort of enlarged, elastic approach to EENS common in the Novus Ordo-- describing the Catholic Church as the "privileged path" like Robert Barron did to the Jєω Ben Shapiro-- is certainly a complete failing and dereliction of duty. 

Quod and Lad,

I'm quite open to it being heretical; not recalling exactly what was said (but just the tenor and gist of it) I didn't want to overstep my memory.  As Byzcat said, heresy requires a direct doubt or denial of some de fide teaching and in this case I was not sure how direct it was.  Which is a point simply to how one categorizes what Barron said.

That's why I said objectively heretical.  If in point of fact the position articulated guts the dogma of any meaning, then it's heretical.  It reduces EENS to a "meaningless formula" and effectively guts the dogma.  If some atheistic Jєω like Shapiro can be saved, then there's no one who can't be.  So EENS becomes a mere tautology.  You can't be saved unless you're in the Church, but if you're saved then it must mean you are in the Church.  But anyone can be saved.  Therefore anyone can be within the Church.  It turns EENS into a pathetic joke.

That's why I said objectively heretical.  If in point of fact the position articulated guts the dogma of any meaning, then it's heretical.  It reduces EENS to a "meaningless formula" and effectively guts the dogma.  If some atheistic Jєω like Shapiro can be saved, then there's no one who can't be.  So EENS becomes a mere tautology.  You can't be saved unless you're in the Church, but if you're saved then it must mean you are in the Church.  But anyone can be saved.  Therefore anyone can be within the Church.  It turns EENS into a pathetic joke.

To be clear, I don't believe any atheists can be saved.  

The meaningless formula thing comes from an encyclical from Pope Pius XII.  Which as far as I understand, wouldn't be infallible.  So I'm not sure how that could be used to determine that particular views of EENS are heretical.

And to be clear, again, I'm not defending Barron, just trying to understand how exactly we're distinguishing heresy (outright condemned by the Church) with merely extremely implausible imprudence