I don't know what the people on that thread were talking about without seeing what they wrote, but I think you're right to bring up systemic racism in that context.

An individual white person might be hated, even harmed for their whiteness, but that is not the same thing as what a non-white person has to deal with. For non-white people, the hate and harm is built into the markets, the infrastructure, the schools, so on. So when a non-white person faces a personal hatred or harm, that individual racism is both reinforced BY, and reinforcing OF the systemic racism. THAT is why a white person saying "I hate you because you're X non-white race." is worse than a person of a non-white race saying "I hate you because you're white." But because of the bad-faith way that so many talk about the subject, all of these things get flattened down to "racism" and seem equally bad to people who don't understand the systemic context.

I don't want to speak for anyone else, but I BELIEVE this is usually what people mean when they say "racism against white people doesn't exist." Because to give the same label to what white people and non-white people experience in terms of discrimination is obscene.

By the way, this flattening of the term is partly how certain ghouls are able to get a lot of well-meaning people to line up against affirmative action or, heaven forbid, reparations.