One more nail in the coffin for Internet anonymity.
In essence, what I'm saying is that a card-carrying member of some radical movement (whichever movement you or I hate the most) perhaps should be shunned by people in all kinds of social activities because of their beliefs, but IMHO as long as they aren't breaking the law, they still should have the right to be a part of the society and receive core services which require interaction with it, namely, public services, education, jobs, housing, etc.
We have drawn a line in sand upon crossing which people are excluded from society, and that line is criminal law if determined in due process. And before crossing that line people should have the right to not be discriminated in employment. If most of your coworkers hate you because you come from the "opposing outgroup" where there's mutual hate and perhaps a history of violence between your "tribes" - too bad for them, both you and them should still have the right to work there.
Your employer declining to continue your employment: freedom of association
Advocating for a university to not host your talk: freedom of speech
A university not hosting your talk: freedom of association
and so on.