You cannot reason someone out of a position they did not reason themselves into.

That's merely an assumption based on a stereotype you have about people like this. Just because reason may have failed with other people like that in the past doesn't mean it's not going to work with this one, especially if you haven't even tried to reason with them and immediately go for the bigger gun of ostracism (i.e. firing).

It is not reasonable to deprive someone of their source of income for having an opinion you don't like. It IS reasonable to tell them that their opinion doesn't belong in the company chat, and give them a warning that disciplinary action may result if they do it again.

Nobody else should have to put up with an uncomfortable work environment, social club, or anything else, because we have to make accommodations to be tolerant of bigots.

You're excusing hatred with bigotry. The same argument could be used to exclude transgender people.