If you a man or a woman, there is a difference of everything in your world. Like a woman can do things a man can't and vise versa. Like having kids for example. But skin color to me is meaningless in everyway. There is minimal difference between for example a black man and a white man. That is the skin color and only that.
Usually someone who is uncomfortable with their skin color is responding to the prejudice of the society around them. A peson uncomfortable with their gender identity usually feels this right from the start and not because of any societal issues. But anyone should be able to change body parts they're uncomfortable living in.
If I am a men and want to be a female, why is it more socially accepted than wanting to be white or black? - Both cases are about not wanting to be the way you were naturally born? I don't see the difference at all. If people are allowed to be men or women, then wanting to be black or white should also be allowed.
When it comes down to it, being male or female, or being whatever colour, are biological states of being. For someone to have dysphoria regarding either is diagnosable as a disorder.
My only question would be on where it would come from. Neither have a good causal foundation for how it would happen, but at least there is speculation as to how it CAN happen with gender dysphoria, with the inter-mix of horomones in the womb, during development. Colour, on the other hand, is simple skin pigmentation. There is no point in the womb where hormones combined to pigment your skin, so it doesn't seem like there could be an actual, physical causal link.