There are a lot of posts below, not so much agreeing with Chris' point that racist is "close" to nigger as an insult, but seeking to reformulate the argument to make it work.
This is amazing to me. We all have a place where conversation ends, and we begin to doubt that dialogue is actually the answer. The contention that "racist," if unsubstantiated, is close to "nigger" is, I think, mine.
The Holocaust is the epitome of industrialized hate, antisemitism invoked to genocidal ends. Moreover it exists within a shockingly ancient, and shockingly consistent tradition of state-sponsored terrorism against Jews. Hence to be labeled an antisemite is to be placed within one of the most evil, and trenchant, traditions in Western History.
Yet if a Jewish person called me an antisemite--or a Nazi--not because I'd done anything to warrant it, but because they felt like it, I simply can't see myself asserting that that's almost as bad as me calling them a kike, a hook-nosed Jew, money-grubbing Jew, or any other anti-Jewish slur.
If only because I have no sense of the other side, my tongue would be stayed. But more than sheer modesty, I'd understand the difference between attempting to dehumanize someone, to reducing their entire person to the ugliest imagery I can muster, and dishonestly ascribing to them a set of noxious beliefs. One says that you have some dangerous ideas about humanity. The other doubts your relationship to humanity itself.