What does “Your hair is so white now, it can talk back to police” mean?

Solution 1:

I don’t understand why you can talk back to police when your hair is white.

The key here isn't that you can talk back to the police if your hair is white, it's that the hair can because it is white.

Ignoring recent events with people being shot by the police, it's generally a (possibly accurate) joke in the US that the police treat white people better than they do black people, and therefore that it's easier for white people to get away with minor things (such as talking back to a cop) than it is for black people.

The speaker is just personifying the hair, and implying that white people can get away with talking back to the police, while black people would be arrested or harrassed.

Solution 2:

The speaker was addressing a black person and, considering recent incidents between the US police and black citizens, it is supposed to be black humor. ("white" would make the police think twice before shooting and one would have a chance to talk back) That's how I understand it. What doesn't fit here is that Mr. Obama should have found it funny.