Steve's parents were definitely Reagan Republicans mainly due to his fiscal policies that allowed them to exploit people and make more money. But that also means whether superficially(or worse genuinely) were part of that "moral majority" bs. So imagine Steve, late middle school aged being stuck going to some fundraiser event his parents are hosting during Reagan's first election campaign.
He would have to sit and listen while people alluded to "family values" and other euthanisms for being anti-queer. And Steve may not always be book smart but he is not stupid. His parents and all their friends were affirming that him liking anything but women was wrong and gross and un-American. So he hid the fact that he liked guys in his class as much as girls. Focused on only his romantic feelings for girls. Wouldn't shut down Tommy when he made homophobic remarks even though it killed him because not only had Tommy been his best friend since the 5th grade, but he had also been his first crush.
But as he got older, and grew close to The Party and the other older teens, he started to feel like maybe his parents were wrong. Maybe people like he and Robin and Eddie and Nancy and Jonathon and Argyle and the kids deserve to be themselves, deserve to love whoever they want. And eventually he finds his romantic soulmate in Eddie, and they are so happy together.
Meanwhile, his parents left Hawkins permanently after the "earthquake. Ended up selling the house, sent Steve some money for a security deposit and first month's rent, and barely have kept in touch since. It's okay, Steve talked to them in obligatory phone calls a couple times a year. He doesn't really miss them. They haven't particularly been there for him most of his life. He and Robin (and later Eddie and Nancy who move into their respective partner's rooms) share that apartment and are happy.
So imagine their surprise in 1988, when they turn on the TV, they see their son on TV kissing the Munson boy at a protest in Chicago over the government's response to the AIDs epidemic. Standing next to them is all their friends, many in queer relationships of their own. Eddie is holding a sign saying Silence=Death, and Steve’s sign simply says "Fuck Ronald Reagan" And that's how his parents found out he was queer and that he hated Reagan.