Depends: does the public consider this climate denying president to be a supreme dictator or an employee of the public?
Doesn't matter. His policies are to defund clean energy and promote continued fossil fuel use.
It does matter because if the former then the people will sit back and watch, but if the later they will rake the president through the coals until he complies with the wishes of his employer, making any personal views immaterial. That said, I think what your comment implies gives us the answer to the original question.
What if a climate denier became/becomes president? What would be the consequences?
And not just on the planet but more locally: the folks that have to deal with hurricanes or wildfires? What happens to insurance rates? What happens if we stay very dependent on petroleum, and oil prices spike? What happens to people's cost of living (esp. food, which is transported by truck and use oil in fertilizer)?