Given it is a discussion of an entity that is already defined by properties not shared by any other real world entity its seems not just logical, but reasonably, to assume that it differs from them in other ways too.

I tend to agree traits is not an accurate description, but it is a reasonable analogy.

> The trinity relations are not "is a" to begin with, or we'd be having many gods and Christian priests are not into that.

Sayings "priests" seems and off choice of wording. Why not just Christians, or even "Christian theologians"?