As long as the thing they don’t like about your face isn’t it’s color. But seriously American employment laws (in most states) allow for companies to fire people for any non-protected reason (protected reason = gender, race, age, etc). If a co.pany does illegally fire a person it can be a real up hill battle to prove it because at-will is so permissive.
I can’t say a firing like this one sits super well with me personally but it’s almost certainly legal.