According to a recent Pew Research Center report, most Republicans and Republican-leaning Americans (heretofore "Republicans") do not believe in anthropogenic climate change. Does that mean they won't support policies or regulations that reduce green house gas (GHG) emissions? No.
That's because lots of things that reduce emissions also save money, reduce pollution, and slow the depletion of fossil fuels: causes Republicans can get behind. Plus, most Republicans actually agree the climate has been warming; they just aren't convinced that human activity is the primary cause. I suspect those who remain unconvinced about humans being the main driver of climate change are at least open to the possibility, especially given a substantial minority of their fellow Republicans have already reached that conclusion. If people you trust (fellow Republicans) hold an opinion, then maybe there's something to it. The door is cracked open.
Also it's important to remember that many climate change skeptics accept that human activity (specifically, GHG emissions) plays some role in global warming. Many of these skeptics are concerned about climate change; they recognize that reducing GHG emissions is a good idea, because they accept that emissions contribute to warming (whether or not humans are the main source of those emissions). And guess what? Almost half of Republicans report they are at least somewhat concerned about climate change. To be concerned means to want to do something about it.
When you add it all up, why wouldn't Republicans want to find ways to reduce GHG emissions? Okay, so that's a hypothesis masquerading as a rhetorical question. Let's test the hypothesis by looking at what state governments are doing about emissions. Next.