But making public your support for Trump — or the KKK, or NAMBLA, or Hacker News — is a completely different thing. You can and should be judged on the basis of the ideas and opinions that you promote.
On Liberty: Society can and does execute its own mandates: and if it issues wrong mandates instead of right, or any mandates at all in things with it ought not to meddle, it practices a social tyranny more formidable than many kinds of political oppression, since, though not usually upheld by such extreme penalties, it leaves fewer means of escape, penetrating much more deeply into the details of life, and enslaving the soul itself.
That reminds me of the quotation:
"A new idea is a beautiful and fragile thing. Attack people, not ideas."
I don't know who said that first, but I love that quotation. It mocks itself (and other witticisms), and at the same time reminds you to focus your energy attacking ideas rather than people.
In extreme cases, someone can have a lot of bad ideas and you need to challenge them personally. But that's only in extreme cases, and doesn't apply transitively to supporters of the person.
Usually people are judged based on the ideas that those who oppose them hold.
Not in the context of your employment, you shouldn't. Really, where does this attitude come from that one's employer should get a veto over everything one does when off the clock? It's usually from people who are always complaining about evil corporations stepping on people's rights, too. I don't get it.