Nothing, and as you point out, many do. At the same time, default is a powerful thing.

I'm a mod for /r/cscareerquestions, and while we're ostensibly non-political, the fact that we try to keep a minimum bar of 'professionalism' means having norms that are somewhat left-leaning. As an example of what I mean, "it's less important for women to have strong careers than men" is a very common opinion among social conservatives, but we'll ban posters who say things like that because, well, it's sexist and unprofessional. This kind of thing isn't limited solely to right-leaning opinions, but it doesn't tend to be that way more than if it for left-leaning opinions, I think.