This can't possibly be true.
Yes, the term "Nazi" is considered offensive. I recognize that it it a colloquialism and that many people are now able to overlook the roots of the word, but the fact remains. If you'd like to enlighten yourself as to why it's a problem, you may want to read the following links.
A Jewish perspective:
https://www.kveller.com/why-we-need-to-stop-using-the-term-grammar-nazi/
Additional grammar-related sources:
https://www.quickanddirtytips.com/education/grammar/stop-calling-yourself-a-grammar-nazi
https://stancarey.wordpress.com/2015/12/01/what-should-we-call-grammar-nazis/