If you look at people on an axis other than liberal/conservative, you find that the people that object are the same people regardless of their politics. They're the people that can't stand the idea of other people seeing reading/hearing/seeing things, that they themselves wouldn't want to. It's the people that are hurt and scared when they see behavior that is actually harmless to them, but maybe spotlights a difference they don't want to be aware of.

Saying that liberals or conservatives have this to a greater or worse extent is looking at it through the wrong lens.