If they're employed in an at-will state, they can be fired for something like that. No sense needed. The issue lies with the company.
And I disagree. Firing someone for making the OK sign -can- make sense, because it can be a racist dog-whistle. That's the entire point of co-opting an ubiquitous symbol. It may be perfectly fine, it may not; the context matters.
"now they contribute nothing to society even though they are perfectly capable of being productive"
That is simply not the responsibility of a business. The fired person can find another job at a different company if it was such a trivial comment.
"You're going to tell some kid, "Your mom doesn't get child support anymore because your dad said something mean on the web"?"
(If it was really just a mean comment): "Your parent was fired because their employer is irrational. Sucks, but that's life sometimes. <Child>, this is a reminder that getting work is a privilege, not a right, and you should save money just in case you get laid off as well. Companies are not loyal to you."
(If it was actually bigoted / hate speech): "Your parent was fired because they put out bigoted statements online, and their employer didn't want to keep them on their payroll. <Child>, this is a reminder that getting work is a privilege, not a right, and you should save money just in case you get laid off as well. Companies are not loyal to you."
If a company fires people like this, they'll get flak and probably burn out as the smart/talented people move to more stable companies, etc. Making people much harder to fire will just make companies worse; I really don't want to have regular jobs function like government ones where terrible people stay around because it's too hard to fire them.