Many Christians in the American south believe it's a hoax. However, it's interesting to look at the different strands of politics with them. Do they believe it's a hoax because they are Christian or because it's what many Republican leaders tell them? They tend to go all-in on politics and believe everything they hear from the side they've chosen even without understanding the arguments.
As an example, I once had an old man who would hang out at the place I worked tell me that rich people needed a tax cut. He was probably living from one social security check to the next but the two things he trusted most were his god and his Fox News (he might have considered Fox News to be the Holy Spirit aspect of the trinity, I'm not sure).
What would happen if Republican leaders suddenly said climate change is true? It would be very interesting.
You do bring up some interesting points and it's difficult to answer, you could easily write a thesis on this subject. I'm not even sure if Republicans are the cause of this attitude or are just the result of this attitude, so it would be very interesting to see what would happen if leaders suddenly changed their tune.