It doesn't matter if they enshrine things or not, they do not create rights when the "enshrine" them.
Sodomy is a disgusting act and a sin, but it does not violate rights, therefore it is between God and the sodomist. Flag burning is certainly a right, albeit an insult to many people. Abortion is murder, it violates rights, it is not a right.
Further, playing into the hands of those you oppose is a bad strategy. You concede their point when you bargain their ability to create rights out of whole cloth against yours. Not to mention that if you are going to defend rights, you would be better served to defend the legitimate ones we have which are currently being usurped or on the way to being usurped.
Bob Bork and Bill Rhenquist would disagree with you. We can safely assume Sam Adams and James Madison would laugh at the idea as well.
On the other hand, Ruthbadgirlginsberg, Steve Breyer, Dave Souter--and probably his boyfriend-- would be on your side.
I'll take the judgement of the former group over the latter. The fighting words doctrine worked fine up until 1986. There was and is no need to revise it.