So ok, I think one interesting hypothetical would be that someone in your company publicly "likes" the Aryan Brotherhood Facebook page (though I doubt such thing exists and it would likely be some derivative). Could you sack your employee for being a total racist?

I guess it would technically boil down to what the actual impact on people at work would be. Do you have an employee who is an ethnic minority who feels threatened by this? Do they actively threaten them? It is complicated.

If we truly see ourselves as liberal and tolerant, how exactly should we react to someone who is openly part of an intolerant group who is offensive to our viewpoint? Do we draw a line somewhere?

Lots of questions, ethical and legal.