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Now that we have established that Catholics can no longer hold to the opinion that explicit belief in the existence of a rewarder/punisher God can suffice for supernatural faith, let us expand on that.

What is supernatural faith?

If the authority upon which we base our assent is human and therefore fallible, we have human and fallible faith; if the authority is Divine, we have Divine and infallible faith.

There are two aspects to faith.  1) a supernatural object of faith (as per Vatican I) and 2) a supernatural formal motive of faith.

Let us now take some concrete act of faith, e.g. "I believe in the Most Holy Trinity." This mystery is the material or individual object upon which we are now exercising our faith, the formal object is its character as being a Divine truth, and this truth is clearly inevident as far as we are concerned; it in no way appeals to our intellect, on the contrary it rather repels it. And yet we assent to it by faith, consequently upon evidence which is extrinsic and not intrinsic to the truth we are accepting.  But there can be no evidence commensurate with such a mystery save the Divine testimony itself, and this constitutes the motive for our assent to the mystery, and is, in scholastic language, the objectum formale quo of our assent.

So we have a supernatural object to which we assent based on extrinsic evidence, i.e. the authority of God revealing.  That a priori belief in the authority of God revealing constitutes what's referred to as the formal motive of faith.

But that formal motive must be based on an infallible and certain authority.  We cannot have the certainty of faith regarding the object of faith without an authority that's known with the certainty of faith.

Protestants and others who refuse to accept the teaching authority of the Church base their adherence to these truths on "fallible and human" authority because their ultimate criterion for faith is their own private judgment rather than the authority of God.

Consequently, even when accepting truths such as the Holy Trinity, these are not known with the certainty of supernatural faith unless accepted on an authority that has the certainty of faith.

Consequently, there can be no supernatural faith outside the Catholic Church.

Consequently, only Catholics can be saved.  I prescind here from any discussion regarding BoD for catechumens.

No response for ANY of the BoDers?

It shouldn't be that hard to follow the majority theological opinion (including St. Thomas Aquinas) and say that no one can have supernatural faith without explicit belief in the Holy Trinity and the mysteries of the Incarnation, and that pagans, infidels, Jews, Muslims, etc. who do not explicitly believe in these revealed truths cannot be saved by BoD (since they cannot have supernatural faith).

In fact, given the evidence from Vatican I, it shouldn't be that hard to condemn the minority opinion as untenable.

If you find it hard, you have to ask yourself why.  You need to do some soul-searching and see if it isn't because you just have a hard time emotionally coming to terms with and accepting that such people cannot be saved.  Emotional things like that (as admitted by Father Cekada) can be an impediment to honestly seeking and being able to embrace the truth when found.  St. Thomas teaches that since truth is the natural object of the will, error usually comes from the will, from an unwillingness to accept the truth.  You need to do some soul-searching and you need to pray for enlightenment.  In holding such things, you're barely hanging on to the Catholic Faith with the skin of your teeth and risk losing it altogether.

We need to heed the popes who taught that there is one Faith and one Church, outside of which there can be no salvation.  We need to stop "emptying" the Cross of Christ of its meaning.  We need to stop propagating the pernicious error that it's possible for someone to be saved in the profession of any religion.  We need to stop "dissolving Christ".