It isn't so much politically correct as it isn't really considered incorrect. Nazis are generally a non-topic in the US; if you want something offensive you need to use particular examples (e.g. Hilter) or specifically refer to The Nazis.
That being said, some variations have their own offensiveness attached (e.g. feminazi) but my hunch is that this has more to do with the usage of the term than the inclusion of "-nazi."
The internet tends to care less about political correctness and the phrase "grammar nazi" is more common when you can pick apart the spellings of there/their/they're and your/you're. I advise against using it in person until you hear someone else use it.