No it doesn't. You can be religious and think ID is a bunch of hooey. This isn't an either-or proposition.
Of course it isn't.
But it IS "an either-or proposition" if you insist on a LITERAL interpretation of The Bible.
You can be religious and understand/accept evolution and understand that "The Garden of Eden" was a parable.
You CANNOT believe that The Garden of Eden was a physical location on Earth and understand/accept evolution.
Insistence on a literal intepretation is not a pre-requisite for believing in Adam, the Garden of Eden, eternal sin, or Jesus dying for our sins. You've resorted to a straw man. I don't insist that all the details were exactly as reported. I do believe in the vast majority of the Jesus narrative. I'm open to there having been an actual physical Garden of Eden in some form or fashion, and possibly there being a key ancestral couple like Adam and Eve.