I think the social acceptance of LGBT worked a bit different, largely because they’re not visible as such, unless they want to be, i.e. “come out”.
So, straight people discover one day that the person they like as a friend, relative, acquaintance, movie star etc. is indeed gay. But at that point, they’ve had plenty of opportunity already to find out their prejudices are untrue.
It doesn’t work that way with racial minorities. Nobody comes to like someone and then suddenly discovers this someone is black.