I got the feeling it was more of the fact he got fired from his job not because Harvey was GAY.
Agree to an extent. I believe Dan White was envious of Milk's organic political skill, on a pathological level. He had an inferiority complex, Milk was getting national notoriety, while his career as a politician was going nowhere.
So, he may have thought to himself, how is this 'lowly queer' making me look bad? He never seemed to grasp that Harvey was literally fighting a life or death fight for homosexual rights, it wasn't just his political 'issue'.