There is limited information about either of them posted publicly, so while a few of his father's internet "footprints" suggest he is a liberal, the same cannot be said about his mother.
His mother is a registered Republican. In other words, registered as a member of the party more accurately named the Radical Right Wing White Supremacist Party. Those who reject the basic principles of that "Party" have long since left it to register either as Democrats or Independents. Or to simply not vote at all.
Regardless, Gedron describes in several posts on Discord a rather horrifying incident involving a cat that (apparently) his mother knew about.
From The Washington Post
Walking into the garage one night, Payton Gendron found a feral cat attacking his own cat, he wrote. Gendron repeatedly stabbed the feral cat with a knife, then smashed its head on a concrete slab and finally chopped off its head with a hatchet, he wrote. He posted a photo of the gray-haired cat, decapitated and bloody on the ground, surrounded by wet leaves.
“I called my mom and she gave me a box and I dug a shallow grave in the backyard,” he wrote on March 25. “Honestly right now I don’t feel anything about killing that cat. I thought I would be in pain but I literally just feel blank.”
It's not clear how much he told his mother, but it is hard to believe that she didn't grasp that her son had killed that cat, tho the manner in which he did so may not have been disclosed.
It isn't at all clear to me that his radical political leanings were completely unknown to and not even suspected by either parent. At best they were negligent. A young person does not come up with those viewpoints SOLELY via the internet. And even according to Payton himself, his parents knew something was up at the very least in April (quoted above).
He may have gathered most of his thinking from "the internet," but the internet is actually a quite diverse arena. There has to be an originating drive from him OUTSIDE the internet. There has to be something in his family background that made him seek it out and be susceptible to it.
Something has to be very wrong in that family. What it is is anyone's guess. But it's hard for me to believe they were completely unaware of his activities. And if they were, that is indicative in and of itself with a not-very-healthy family environment.
Regardless, none of that in any way negates my assertion that mental illness does NOT explain his deep and abiding racial hatred.