Last week, I was on a political group on FB and someone mentioned this word. When I looked it up, its definitions indicated it was the opposite of racism. The word means, in simple terms, that "Person A feels racially inferior to Person B and perhaps even wants to be the race of Person B". It starts with an "m" I think.
One word that fits is supremacist:
An advocate of the supremacy of a particular group, especially one determined by race or sex.
While it's usually used for people who believe their own race is superior to others, it's also used with people who aren't that race. For example, one might call someone a black White supremacist or a white Black supremacist, although there is apparently another (likely pretty offensive) term for the former (see LaShanda's definition).
In addition there are other words that fit but are more about hating one's own race rather than liking a certain other race: