What do members of the BB hold as separating them from Papists?

[Aaron]

At NO time is the passage suggesting that the believer is a literal descendent of Abraham. We are all JOINT HEIRS of the promise and hope of the believer - just as was Abraham.

I agree. We are not descendants according to the flesh. However, those of faith are the true children of Abraham, Jew and Gentile alike.

For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God. Rom 2:28-29​

BUT, Abraham was the father of physical nations in which the believer has no (or should have little) care.

That's over and done with. A greater than Abraham is here.

Our relationship to Abraham is as the same Heir of promise, the same blessing of promise. - Salvation.

Agreed.

The passage is stating that the SAME justification given to Abraham is the SAME justification given to Gentiles.

Agreed, but more, that was the Promise.