Grammar Nazi is made by a bunch of lily white people who are KKK at heart. So I think someone who emphasized grammar should be a grammar Klansman or a grammar segregationist. That's a more fitting term. "Grammar Nazi" is a Scandinavian invention used to demean Germans. And others too!
Grammar is what makes a language, and you should respect it.
There are plenty of people who take no notice of grammar and look imbecilic as a result. It really does depend whether you want to appear as an imbecile, or as intelligent person, and when applying for a job for example, this is really when it pays to show you know the real basics of your own language.