Nazi is an emotionally loaded word, because of the fact that there are people alive today who were directly affected by the Nazi regime. I can't fault people for being sensitive to it, and I'll do my best not to use it lightly around people who find it offensive.
That said, I don't think it's fundamentally wrong to use the word "nazi" the way it's commonly used today, simply because we're not talking about the Nazi party of Germany. The day Seinfeld aired the first episode featuring the soup nazi, a new definition was attached to the word nazi, one that had nothing to do with Hitler and his followers (though it's related in meaning, and the basis of the new definition).
A fantastic parallel is the word crusade. Its original definition is "holy war," specifically the holy wars over the middle east during the middle ages. However, people also use "crusade" to mean a campaign for a cause; this definition is found in the dictionary in addition to the traditional definition. Though I'm not an etymologist, I'd be willing to bet that this definition came about by widespread use of "crusade," to mean "campaign for a cause," exactly the way people are now starting to use "nazi" to mean "someone who is obsessive about somthing."
A few more examples of words with tragic meanings that are used by convention in lighter ways
I'm sure there are many more examples.