There are characters where I care about race, but more often than not it's not that much of a concern. I'd keep Emma Frost white (and blonde). My inclination is for Jean Grey to be white, but if she does need to be racebent (not that I could say why she specifically would need to be), I'd rather they make her Asian or Hispanic rather than black. I'm also inclined to keep Rogue white, if only because they're already probably making major changes to her compared to the version I know/like, and it's just another addition to her being changed. However, if she does get changed, oh well. Other than that, I can't think of any white X-Men characters where it would be a sticking point for me.
As for the idea of Mystique being transgender, I'm against it, and I don't think it'll happen, anyway. If Marvel does go there, I don't think it'll be with a character with so much general audience exposure.
However, putting that aside, I just don't think it would work. If you make Mystique a man in a woman's body, then you've made a female character male for the sake of diversity. If you make her a woman in a man's body, then you've changed her default blue appearance to male and put her in a situation where she'd never want to take that form. Unless you have her a blue male who transforms into a blue female instead, but then her "real" form wouldn't be much more real than any other form she takes.
I also think it's important to not have conflict between the metaphor and the thing it's a metaphor of. For example, you can have racial minority mutants, gay mutants, disabled mutants, but you don't want to depict discrimination against those groups because...if you want a story about discrimination against a real group, you can make such a movie, but if you want to deal with it through a metaphor, having the real thing there just gets in the way of it. It's not good for mutation to be redundant with or in conflict with the explicit real world issues.
People who have a phobia about being touched might relate to Rogue, but if you make her have that phobia, then it doesn't matter as much that her mutation prevents her from touching people because she doesn't want to/can't touch them, anyway. And it prevents people with that phobia from dealing with it from the safer vantage point of a metaphor if it's also explicitly there on the screen and all too real.
Bringing it back to Mystique, her changing forms could be seen as a metaphor for hiding your identity from an unfriendly world. She disguises herself as people who are more trusted than her, more desired than her, more empowered than her. If you make her someone who uses her power to change herself from the form she doesn't see herself as, you've killed that metaphor. You've made it into wish fulfillment for transgender people, the ability to magic up a new body at will, when the X-Men isn't about wish fulfillment. If there were to be a transgender mutant, it should be someone whose power has nothing to do with that.
