Here's the problem: at least in SV, you're going to be restricted to a sub-set of very narrow beliefs which are acceptable to express. I may hold a personal belief that, say, trans-sexuality is not a "real thing" or ought not to be treated with surgery. Do you honestly believe I'd be able to express that in such an environment, as much as someone who believes it is "a thing"? You may believe my belief is just too "in-tolerant" or "bigoted" to be expressed, but who are you to be the arbiter thereof?
Now let's take the other side of the coin. If you work in the energy industry, heavy manufacturing, etc., you probably couldn't express support for trans-sexuals without having problems. On the other hand, you'd likely have no issue saying you didn't believe in such a thing. I know someone in energy who wore a rainbow flag pin during one gay month a few years ago; he wasn't fired, but many of his superiors became noticeably cold toward him and he left after realizing he probably couldn't move up at that company. Again, why ought that to be the case?
The biggest issue is that when people start talking politics, you are expected to participate. Some one looks over and says, "Hey Big Chungus, what do you think?" In such a situation, I cannot reasonably say, "Oh, I have no opinion." Certain issues are simply so partisan that such a response, even in the rare circumstance that it is true, will anger both sides and damage me.
So, I avoid talking politics at work and try to work at places where others do the same. People I work with generally never know my politics. I am more than happy to bloviate about political stuff with friends and family, or to go be mad online after work. At work, it is best to stay non-partisan.