Obviously the free market solution to this would be a private airline that only allows natural-born US citizens as passengers, and refuses to allow Muslims to fly, ever.
I don't know if that's legal -- I doubt it -- but it'd make a ton of money.
If they can violate the 1st, 2nd, 4th, and other amendments under the guise of "airport security", why can't they violate the 14th also (or better yet- instead of the others)?