The law doesn't really apply in this case.
I agree with those who say it sounded like the decision was a weighted scenario. Ultimately he doesn't have a job now, because he's not an amazing player. We could probably rattle off several dozen football players who would still have a job if it were them who had done this instead.
He's a mediocre player and no one wants to pick him up in with the combination of -
A: He's controversial, (which didn't really bother them, they could have asked him to stop if they wanted to)
B: With him only being mediocre why bother with him at this point
Except no one gets fired for being a fascist.
I imagine if their bosses discovered they were at an Antifa rally fighting on either side, or had gotten arrested for something like property destruction, they would be fired. Most employers do not want you to be recognize/representing them in public doing stupid shit. Some major companies require you to let them know when/why you've been arrested (they'll fire you if they find out you didn't) so they can decide if they still want you working for them.
As for being fired on ideology alone, Nazi and KKK ideals are unlike most popular ideals. If you are actively one of the two, most employers would fire you without blinking, and no there should be no laws to protect them.