Earlier quoted context omitted.
Illegal and unconstitutional. It's not up to the carries to dictate which phones work on their Network. That's the reason for standardization of network protocols Do you really want, hypothetically, a phone maker, say Apple, to get into a sweetheart deal with AT&T and make phone service on non Apple IMEIs unreliable? Or for AT&T to target certain political, religious groups ....
Unconstitutional? The carriers are private companies, I'm not sure what in the Constitution would apply. (I'd agree with "illegal" for the same reasons Ma Bell can't require that you use one of their phones on their phone lines, but that's just because lawmakers decided it should be illegal; they weren't constitutionally obligated to make it illegal.)
So no, they can't just do whatever the hell they want.
With that said, They SHOULD have a surcharge for ZTE phones, if they are hostile to their network.