I'm sure you're correct that ideas are more fluid than gender, and this is a major aside... but I'm not convinced ideas are quite as fluid as they seem. Have you felt life would be a lot easier if you didn't believe something was true?
I've read that some students and faculty on college campuses feel like "closet" conservatives (this certainly isn't the only place where people feel at risk for their ideas, and it certainly doesn't always go in this direction).
But I'm not sure people are 100% in control of what they believe. Sometimes, you look at the data, you consider the analysis, and you reach a conclusion that you know would harm friendships, alienate you from your community, and so forth. This often happened in religious contexts - for example, I'm sure a lot of people who were/are atheists in environments where this is a socially abhorrent idea aren't pleased with their conclusion, and keep it very close to their chest, revealing this only to very trusted and close friends and family. But this sort of belief isn't really voluntary - it's more mutable than many other traits, but it's not entirely fluid, either.
In short, I think that ideological minorities may have something in common with minorities in general - though not everything in common. For instance, it's a lot easier to hide, though being forced to listen to and agree with things (either explicitly or through your silence) actually does take a psychic toll after a while.