If your politics, or the beliefs of those who share your politics, make your coworkers feel hurt, scared, and angry, then I see absolutely no reason to bring them to your workplace. It's basic human interaction 101. And sorry, but insisting that people grow a thicker skin won't work, because that's not how people operate. I discuss controversial topics in person with my close friends, and I don't feel any poorer for…
Let's imagine we work together. I say your politics, whatever they are, make me feel hurt, scared, and angry. Obviously you can't argue with this; my feelings are my feelings and are thus inarguable. Therefore, by your basic rule, you are no longer allowed to even state any of your political beliefs, because such would make me feel hurt, scared, and angry. And it doesn't matter what your beliefs are or how you arrive…
Not really. This only works if your opinions are part of the current zeitgeist. If not, then nobody will really care what some loner is hurt by, and will probably just avoid talking to you, period.
> At a certain point, people do need to be told to grow a thicker skin.
OK, but that doesn't work. It only makes people angrier and even more determined to exclude you.