I don't know about the 90s specifically (I was 6 when the new millennium started!), but people were definitely talking about "politicial correctness gone mad" and the "war on Christmas" in the early 00s.

Here's a comedy sketch from '05 that's making fun of many of the same "woke" concepts we have now:

https://www.youtube.com/watch?v=9u7Z5cNfc9w