The State could argue that parking in the manner you indicate is not conducive to effective use of space... Rational Basis... Therefore, they can restrict parking but it must be to all parking seekers... they can't say One armed Irish midgets only are restricted... but they could make handicap parking available and restrict its use to the obvious handicap these Irish midgets have and others with handicaps....
No, you are again going back to restricting a particular group. That's NOT what is happening. They are enforcing the same parking regs for everyone, everyone is allowed to park. Now some decide they don't like how parking normally works, so they should have the right to park in a different way. That's fine, but the state does not have to have some sort of strong basis for not wanting to redefine what "parking" means.