Being racially abusive is really bad too, drunk or not. But there are some people who say and do things drunk they don't believe sober. And when they apologize (and stop getting drunk), it's only fair to take them at their word.
But if someone is taken in for DUI, and in the process blasts out a tirade of anti-Semitic slurs and threats at the officers, and that someone is a prominent filmmaker whose father is a Holocaust-denying anti-Semite, and that person has not repudiated his father's views, and that person is a member and supporter of his father's crazy church, and that person has made a passion play film of just the kind used to launch pogroms and massacres, it's time for more than just a public apology.
Hey Mel? It's time for a complete turnaround. Stop drinking, stop being racist, repudiate your bigoted family and friends, and spend a decade or so making amends. Or just toss the citizenship and leave, because you're not wanted.