We've gotta distinguish ourselves from the people who persecuted them and kept them down. If we're the champions of equality, civil liberties, peace, prosperity, opportunity, and against corporate welfare, we can begin to break up the monolithic voting blocks of minority voters. Our ideas are right. It's only natural to assume that as soon as we stop alienating them we can begin to winning some of them over. Remember that people are individuals, not drones in a collective.
Acceptance and education...that's how we win. We can do this!