A lawsuit wouldn't win IMHO.
The airports are already government property, paid for by tax dollars, yet they allow all sorts of differences between passengers already. Frequent flyer check-in lines; baggage lines, even airplanes that are inspected by the FAA which contain first class seats in them!

This is exactly the right thing. The feds should SCREEN each passenger equally, and that's all the job that they are being paid to do. They traditionally don't control the check-in lines, the boarding gates and passenger boarding order, or whether the airlines make other preferences (on government property, the airports) for some types of flyers who either pay more for their tickets, fly frequently, or even happen to be congressmen!