This claim could simply just be an opinion, but I believe there is enough evidence on record to label it true. It's important to note that these characterizations reflect documented public statements, not speculation of personal beliefs.
Firstly, Kirk's organization Turning Point USA kept a Professor Watchlist of university professors who promoted ideology that he did not agree with, with specific tags for feminism, LGBTQ rights, "racial ideology" etc. Ms. Magazine detailed a number of such professors and journalists who purportedly faced consequences and/or received threats because of their being on Kirk's watchlist.
The Guardian has also reported on his remarks, among them his comments on women and reproductive rights. He is so anti-abortion that on the debate show Surrounded, he said that he would force his 10-year old daughter to deliver a pregnancy that was the result of a rape. He says of Taylor Swift and Travis Kelce's relationship "Reject feminism. Submit to your husband, Taylor. You’re not in charge."
Reuters in its analysis of Kirk's political impact, mentions his thoughts about affirmative action, i.e. that Black women (e.g. Ketanji Brown Jackson or Michelle Obama) don't have the brain processing power to be taken seriously, and that they had to "steal a white person's slot to go be taken somewhat seriously," or that if he encountered a black woman working in customer service who he deems "moronic," he wonders if she is there because of her excellence or because of affirmative action.
The New York Times expands on Kirk's ideas about race in their review of his beliefs, noting "Mr. Kirk believed the Civil Rights Act of 1964 was a destructive force in American politics, calling its passage a "mistake" that he said has been turned into "an anti-white weapon." He also blamed the Rev. Dr. Martin Luther King Jr. for the law and was highly critical of the slain civil rights leader, calling him an "awful" person."
As for his thoughts on the LGBTQ community: He said stoning gay people was "God's perfect law" in a podcast with Jack Posobiec. On his show, he has said there is a direct connection between transness and inflation, without providing any evidence. In an interview with Riley Gaines, Kirk suggests that society "should have just took care of" trans people "the way we used to take care of things in the 1950s and 60s" — which independent journalist Erin Reed notes included lobotomies, shock therapy, and involuntary institutionalization. In a September 2023 speech he said that trans people are "throbbing middle finger to God," and during that speech he directly addressed University of Pennsylvania swimmer Lia Thomas, a trans woman, deadnamed her and told her "you're an abomination to God."
Taken together, these statements suggest Kirk's views toward these groups range from openly antagonistic at best to advocating for their elimination at worst.
