Herein lies the basis of the alt-right's culture war BS. The entire thing is resolved by accepting that systematic racism, sexism, xenophobia, homophobia, and other forms of discrimination against certain minority groups are alive and well, as well as accepting that that's a bad thing. But most people don't see anything past overt hate crimes (mainly assault) on the basis of social identity to be racism/homophobia/etc. Then, with that view, their rationalization becomes that all racist actions are on an individual level, that the individuals or groups perpetrating killings of minorities are the only problem and they're exceptions which don't appear enough to warrant a major response anyways, and as a whole society doesn't have a problem with racism or sexism or whatever anymore and there's not much society and the government can/should do to stop it. These people genuinely think that, and it's easy to see how you jump from that to "<insert policy which addresses institutionalized discrimination> is discrimination against white/straight/cis/male people". To them, it's "systematic racism/sexism/homophobia doesn't exist, and if it does, it's not enough to be a big deal, so any correction to it is bigotry".
Libertarians' play on this says that the "free market" would stamp out bigotry because it would totally be unviable, because human beings are rational and the people with the most voting money wouldn't support discriminatory business practices... since, again, the bigots are a few select people who the population would boycott. The class-based private education and lack of public education would totally mean more people would grow up to be less bigoted too. Making it illegal to discriminate in business would only hurt the poor business owners who want to ethically discriminate based on identity!
Then, on a different corner of politics, you have the leftists who genuinely take "no war but class war" as a description of what's happening – it's a phrase originally meant to invoke the idea that we shouldn't be marginalizing groups or fighting any war except a class war, and that racism/sexism/etc. are useless infighting – but some ("tankies") have taken it to literally mean that the only real oppression in our society is class-based, and "identity politics" and working on systematic discrimination are how the capitalists keep us distracted, so we shouldn't worry about that.
I've seen the first view on Lemmy a lot in the past when it comes to specifically sexism – the site's largest demographics (young nerdy men) makes it unsurprising, but it's still a bit shocking to see considering the left lean of the site. I think it's gotten a lot better ever since a few months ago though.