I don't think being pleasant has anything to do with this. Perhaps you meant professional?
Assuming that, what if someone is professional at work, but often says at work that they believe black people should be lynched and are subhuman. Is that ok? If it isn't acceptable, why isn't it?
You're welcome to assume anything you want about the account and its nature, I simply don't care.
If it's my personal belief that I am duty bound to try and get this person fired and find legal ways to ruin their life would you be supportive of that? None of this activity would be carried out at work.
It's just a thought experiment - not sure why you need to be talking about trolling.
So, if this person is professional at work, then you come home, and watching the news, you see a report about a neo-nazi parade, and there this person is, literally on-screen, shouting "burn the niggers*. Is that also ok?
Of course, this is an extreme example, I'm just interested in understanding where the line is, or indeed if there is one, in the minds of people who think it's ok to express any opinion without there being any consequence.
So if your co-worker believes that, for example, black people and gays are subhuman and expresses that view you think that's ok and we should all just put up with it?