In general I agree with you but.....
We are not a secular democracy, we are a constitutional republic, God and Creator are all over the Declaration of Independence, and if the writers wanted the separation in there I believe they would have put it there, at least 6 people signed both. The ones that wrote about it in letters wrote about separation of religion, not from religion. I would also argue that a one persons rights are not more important than another persons. All that being said the military is a different animal, those higher ranking than another can tell you to shut up and color.