I understand where you're coming from, but this statement isn't necessarily a truism. You can wear who you are on your sleeve and even be quite extreme, if you're a reasonable person who can build and maintain professional relationships.
I do almost everything online under my real name, and am not optimized for career purposes. It's just me. As a result, I've had my political beliefs and such come up in interviews on multiple occasions. In one case - as I found out a year or so after being laid off - my interview process took a couple of weeks longer than was typical because one of the executives/partners at the company was concerned specifically about my politics. On the other hand, I did in fact get that job (and loved it!) and I've gotten several connections and invitations to apply based upon my discussions. Surprisingly, they seem to be about evenly split between people who agree and who disagree with my stances. I'm passionate about political issues, but I do my best to be accommodating to others and not be aggressive about them.
It would be fair to say that my positions are pretty extreme, too. I'm a political anarchist; Anarcho-Capitalist / Voluntaryist, to be more precise. I am open about that even in professional settings because it has such an influence on how I approach relationships and the world in general. I tend to be a "systems thinker", and see everything as a balance of competing forces. I see the whole world through this lens; everything is influenced by incentives and disincentives. I have exactly one tattoo, a stylized graph of supply and demand.