Are some black people harder on black people than they are on white people because of self hate?

Of course. This is especially highlighted in the police force, where it is said many black officers are extra cruel to their own people in an effort to gain respect from their white peers. This is why you hear lyrics in rap songs like **** the police by NWA disparaging "black police showing out for the white cops". In theory it's very similar to things done by members the "house n*gro" gentry , like Clarence Thomas and Jessie Lee Peterson.