[Winters_Sorrow]

I don't think any mutant can turn their power 'off'
If you mean that they can appear human rather than obviously mutated, well there's plenty of other non-blue mutants who fall into that category. Toad for one, Angel for another. The Morlocks (although you can't tell in the movies) are actually all supposed to be physically mutated which is why they have to live in the sewers in the comics.

In the comics, it turns out that Nightcrawler & Mystique are actually mother & son but Beast's blue appearance is down to effectively experimenting on himself to enhance his abilities.

I think the reason we don't see many obvious mutants in the films is purely budgetory. It's costs a lot of time & money to apply makeup to them. I think it took over 6 hours to apply the Mystique makeup during the first X-Men movie.