In an “at will” state, they certainly can. If you have no negotiated contract with the employer, they may fire you for any reason or for no reason. The exception is state non-discrimination laws, which may prohibit firing for certain reasons concerning civil rights or discrimination, but these vary from state to state, and an employer can always claim that the firing is unrelated to state restrictions, irrespective of the real reason they are firing you, and then you are left with trying to prove what’s in the employer’s head. Why did they really fire you? Good luck proving their reasons were against state law.