I don't think it's chauvinism if my god's name is "God" and I capitalize it, but leave it in lower case to refer to the concept of your god as a "god."
To me, it's like calling my mother "Mom" and saying "your mom" when I mean yours. For me, when referring to my mother, "Mom" is a proper name.
If your god's name is Thor, I would say the god Thor, while mine is the monotheistic god known simply as "God." If another religion also had a god named God, even if this God was not at all like my God, then both would get the capital G. But is there one?
(I'm one of the quaint poeple who capitalizes the pronoun, too.)
I agree.My god (if I had one to call mine.... or is that Mine ) is "God", and I could say of someone else's god 'He believes in a god, but...'. What I believe is chauvinism would be if I said 'You don't believe in God. Your god is Baal [or whoever]'.