I understand where you're coming from but it sounds like you're confusing the agendas of several groups with relatively disparate interests.

In spite of being co-opted as clickbait and misrepresented beyond recognition, safe spaces were originally intended to indicate solidarity with the LGBTQ movement. Making it safe for LGBTQ students to attend school is fundamentally different than censoring speech.

Political correctness is about inclusion rather than exclusion; those seeking to censor history may use the phrase "politically correct," but their actions clearly subvert the meaning. I've been aware of the whitewashing of the U.S.'s involvement in the Holocaust since I was a kid so I'm no stranger to your sentiment but the Religious Right has contributed far more to the censorship of history and textbooks in the U.S. than anyone in the LGBTQ community.