"let's make everything political."
Everything -is- political. For some people, the status quo is amenable to them. For others, it is not. If you want to avoid politics, I think the only real way is to venture into the wilderness and live solo.
"Should you be able to fire them freely because you're not OK with their political beliefs?"
I can't speak for other countries, but the US protects from being fired due to certain characteristics. Aside from that, yes, absolutely, employers should be able to fire employees.
That said, there is nothing preventing said employees from giving said employer bad press, etc. There is nothing preventing employers from getting tried in the court of public opinion.
I don't see why we should expect the government to intervene and say "well, you can't fire anyone, for any reason, ever, as they claim it's retribution for X, Y, or Z". That, I believe, would be referred to by most americans as the dreaded "socialism" that we're so keen to avoid in favor of free market capitalism.