Joe, I too would prefer "America the Beautiful" as our national anthem, for the same reasons you give, but I think it would be hard to persuade the public to accept it as such.

But I see nothing wrong with singing it at every opportunity.

Really, religion in public life is a problem only when (1) attendance is compulsory (as in public schools), (2) when government money is used to subsidize or encourage it, or (3) when government grants special privileges to one religion over another, or religious activities in general over non-religious ones.

I don't know what kind of gathering you had in mind when you asked if you should bring it up, but it seems to me that "America the Beautiful" would be unobjectionable in most contexts.