Whether they can do that or not, in this case it was due to acknewledgedly arbitrary and capricious secret rules dictated by government personnel to the airlines, not decisions by the airlines themselves.

Unless your position is that one of the legally legitimate principles of free business is whether to follow the law or not.

Depends on the business. You cannot have a bar or restaurant behaving like that with some racist/xenophobic/whatever shit like that, you would get your license revoked rather quickly.

Not sure if airliners are regulated like that, but 'free business' is not anarchy by any means, unlike you suggest.