Okay, I don't know exactly how strong or mild Mel Gibson's anti-semitism is. Certainly it exists, and it's not pretty. The fact that he was drunk could have diminished his inhibitions so as to cause him to reveal his true inner feelings, or else it could have led him to make exaggerated statements in a deliberate attempt to shock and outrage his listeners, or perhaps it was some combination of both.
Different people react in different ways to alchohol. I've never been drunk myself, so I can't offer any first-hand experience. But it's impossible to believe there wasn't at least a kernel of anti-semitism for Gibson to even think of making those comments about Jews.
Mel has the right to think what he thinks, and the First Amendment allows him to say what he said. He's not going to be placed in a politically-correct indoctrination camp to re-mold his opinions. But other people also have a right to evaluate him by his statements and alter their opinions of his character.
I personally hope this will be a wake-up call for Mel. Driving drunk at high speeds and getting arrested and facing a barrage of criticism for his anti-semitic tirade might just cause him to re-evaluate the direction his life is going. His apology is a good first step. I hope it's a sincere one, and that he will decide to make changes in his life. If he truly does so, he should eventually be able to rehabilitate his reputation.