So your solution to bring together the left and right wing on climate change is nuclear power? Lets break down every level that is wrong on:
1. "Green people" are a tiny portion of the left wing and have little overlap with the two parties that actually matter in any way.
2. Right wing people are certainly not pro-nuclear, they're pro fossil fuels. You win virtually nobody new if every single democrat went 100% for nuclear.
3. Anti-nuclear people cross the political spectrum roughly evenly... conservatives hate it because it is essentially a government brainchild and because the government has such an interest in the byproducts.
4. People who want to actually address global warming (like Rep AOC) as opposed to simply being pro-nature ARE fans of nuclear. The Green New Deal now encourages nuclear power.
5. Nuclear power is not a magic bullet. It's more expensive than solar and wind. It has the same distribution issues as solar and wind. It requires batteries like solar and wind (although less seasonal storage). It's not because of public opposition, or regulations, or any nonsense like that, it's because nuclear power is fantastically complex and expensive to build. If it was cheap and easy Texas would be dotted with reactors, but instead they have wind turbines.
This whole "nuclear vs. renewables" thing is a relatively isolated scuffle between a minor but visible group of anti-nukes and a much larger but less invested pro-nuclear group that mistakes NIMBYs as the former and is generally low-knowledge on the topic. Enthusiasm for nuclear power is already widespread and generally unopposed. It is not a divisive issue between people who disagree about climate change. It is also not a significantly better solution to climate change than normal renewables.
The goal of climate change denialists is to deny climate change by any excuse necessary. If the hot button topic wasn't the existence of different gender identities, they'd find something else as a wedge issue.