That may be a side effect but it’s not the reason.
The reason is that they don’t want to be told what to do by the government. They want to use the government to tell other people what to do.
“Conservatism consists of exactly one proposition, to wit: There must be in-groups whom the law protects but does not bind, alongside out-groups whom the law binds but does not protect.”
This is about wielding power.
Just to pile on to that thought, it’s also a wedge issue that makes stupid people very angry, and angry people are motivated to be politically active. They will shout down reasonable people, commit acts of violence, and vote in reliable numbers. Polite society tends to avoid political debate, in part because the angry morons show up to disrupt the quiet.