If you are naturally a distrusting person people will pick up on it, just how people will pick up if you're naturallly an open person. (The true trick is realizing that "naturally" can be changed)
Also, what about neurodivergent people who may express their openness/closedness somewhat differently? Are they screwed no matter what?
I won't say you can't do anything to influence your approachability, but I really do think there is a very large component which is essentially fixed, and people rarely acknowledge this (which is annoying).