Framing this as a partisan issue has the causation reversed. The people funding anti-climate change propaganda are the oil and coal companies. They're only "the right" because the places with oil and coal under them happen to be red states, which allows those companies to control those politicians more easily because they have more constituents who would lose their jobs to meaningful reductions in fossil fuel usage. It only becomes partisan once the representatives of those districts push it into the party platform.
You can't defeat that in the long-term by voting the other party in because the nature of the two party system is that each party is in power half the time. The only way to fix it is to reform the Republican platform so that it's one of the issues both parties agree on rather than every administration just undoing whatever the previous one did.
> Perfect example is when global warming was rebranded to climate change, largely by the Right, after which right-leaning politicians have spent every moment saying "See they had to change it from warming to change! They clearly don't know what they're talking about."
Propaganda is propaganda. When it was called global warming they would claim that some places were getting cooler rather than warmer (due to changes in ocean and wind patterns etc.), which was true but not actually any better. If some places get drier and some places get wetter, well, droughts and floods are both bad. More to the point, the ecosystem in each place is calibrated for the previous climate and rapid changes start causing things to go extinct regardless of the direction of the local changes.
But that takes longer to explain than a talking point about how some places are getting cooler and not warmer or any of the other irrelevant nonsense about how temperatures decline every year during the period between summer and winter. Calling it climate change was an attempt to defend against that nonsense, so naturally the industry now spends all day claiming that rhetorical defeat as a victory because that's what propagandists do.
Pitting both sides against each other is how corporations get what they want. The enemy is Exxon, not the people of the state of Nebraska.