You cannot restrict someone exercising a right 'just in case' they might be committing a crime when doing do. Doing so is a form of prior restraint, which is an infringement.
Hmm. Tell me how you feel about warrantless wiretaps.As a law abiding citizen I have no problem whatsoever with being subject to a background check to prove that I am. Haven't been wrongfully accused of being a felon yet.