For me it is okay for a person to be a grammar nazis as long as he/she would correct someone in a good manner. I am sometimes thankful to those humble grammar nazis because I am able to correct my wrong grammar and learn some few tips about how to construct a good sentence. I just don't like "some" grammar nazis people because of them being arrogant whenever they correct someone and they tend to embarrass somebody who commits wrong mistake about grammar. "Some" grammar nazis people feels that they are on top of the world because of their proficiency in grammar. I'm okay with people who are grammar nazis as long as they don't belittle people who are not that proficient in constructing a grammar.
there is nothing really wrong with actually correcting someone's grammar, as long as you are not annoying with. I tend to do it sometimes but mostly with the use of wrong words. why do you use the word nazis though?