with that said, there is an asymmetry in viewpoints that gets lost in the tribalism of ideologies: while both can be short-sighted/misguided (in different ways), many right-wing/conservative positions are about preserving the status of the already powerful, while left-wing/liberal positions are about empowering the disempowered. robin hood, not the sheriff of nottingham, is the hero we generally root for.
On the other hand, selection bias. For every “out and proud” right-winger in the valley getting lynched by an angry mob, there’s hundreds more conservatives, libertarians and even centrists keeping their heads down and trying to avoid political conversations because they know that being their “authentic selves” in such a situation would be a career-limiting move.
Authenticity is not sharing your political opinions with the world. Sharing opinions is about controlling your image.
You can hold political views of any stripe and be well accepted by people whose opinions clash with yours.
Authenticity is not broadcasting your opinions about the world, it's not compromising on your values in order to fit in. Political views are imperfectly derived from values; they're derivative and less important and should be freely modified as you acquire experience, new perspectives, and more information.
Values and authenticity, in contrast, stem from internal discourse and exploration.