What is glossed over in the whole "muslim debate" is that you can't desire something you don't know. This is a philosophical truism.
Indeed, Msgr. Fenton (who supported BoD) stated that the majority theological opinion was that one needs to have explicit faith in the Holy Trinity and Incarnation to be saved (the teaching of St. Thomas, St. Robert Bellarmine, St. Alphonsus) ... so the "Muslim" scenario has little to do even with BoD proper, but more a "faith of desire". So if they can attack us for rejecting the teaching of these Doctors on BoD (clearly they were opining, not teaching), then, guess what, we attack YOU for rejecting their teaching that explicit faith in the Holy Trinity and Incarnation are required for salvation. But, see, the use St. Thomas as a weapon when he supports their position, and then ignore him when he rejects their positions. Intellectual dishonesty in spades.
I hold that the necessity of explicit faith in the Holy Trinity and Incarnation for salvation is objectively
de fide, not just majority theological opinion. Why? Because it was held and taught unanimously for the first nearly-1500 years of Church history. If anything qualifies as an infallible teaching of the Ordinary Universal Magisterium, it would be this, and if this isn't it, then there's no such thing. But in the late 1400s, after the discovery of the New World, a Franciscan and a couple of Jesuits began to float Rewarder God theory, since they didn't want to accept that all these natives in the undiscovered continents had been lost for 1500 years. So they did theology based on emotion.
Let me get this straight. So it's OK for those guys to come along and reject 1500 years of unanimous Catholics teaching and belief, whereas if the Feeneyites reject the theological consensus of a couple hundreds years at most, they're heretics, right? Talk about self-serving contradictions and dishonesty. In point of fact, for about 700 years, all theologians held the position of St. Augustine regarding the fate of unbaptized infants in Limbo, from about 400 - 1100 or so. But then Abelard (who also rejected BoD) became the first to question it. St. Thomas eventually adopted and taught the notion of Limbo, and from there it's become the dominant position. So which theological consensus was effectively inerrant? When they taught one thing for 700 years, or the opposite for the last 700 years?
Oh, and then the Holy Office affirmed the teaching that explicit belief in the Holy Trinity and Incarnation are "necessary by necessity of means for salvation" ... and forbade priests to baptize those who merely professed belief in a Rewarder God. But the anti-Feeneyite SVs hit you over the head with
Suprema Haec as if it were a dogmatic definition, but simply ignore this other ruling from the Holy Office, and ignore also the Holy Office teaching regarding geocentrism (since I don't know a single SV geocentrist). It's pick or choose according to their confirmation bias, where they ignore stuff that doesn't fit in with what they've decided ahead of time that they want to believe.
Oh, and speaking of unanimous teaching of theologians, all theologians unanimously approved of Vatican II and considered it and the NOM to be Catholic ... except perhaps one (Bishop Guerard des Lauriers). These are in many cases the very same theologians the SVs might cite against BoD, but then they somehow believe they all apostasized
en masse on one sunny afternoon in, say, 1962 or 1963, exact date TBD.