I think the controlled opposition theory is certainly true in-part, but it doesn't explain everything.
The other thing is that Republicans don't campaign on policy. They campaign on random culture war bullshit - much of which, while incredibly stupid and a waste of time, is popular.
So, sure, allowing Tesla to dump toxic waste into their constituents' groundwater is unpopular - but their constituents never hear about it until it's already happened, and then the politicians blame someone else.
Instead, they campaign on your parental rights to infect everyone in your kid's class with measels or to ensure your child isn't turned into a trans catgirl by public schoolteachers and trained to use a litterbox, or the competitive sanctity of the women's track and field team, or whatever other dumb bullshit they can come up with.
People can be made to care about that stuff easily. Then the politicians get elected, do some random bullshit culture war legislation to get re-elected, but focus on making their corporate donors happy by allowing them to more effectively fuck over the constituents.