A few things, I think.But, something drives the denying of climate change as a pervasive threat, is it the idea of tax dollars going towards research and climate change initiatives?
One is a way to shirk responsibility. If you deny there are any problems with climate change, you will not feel an obligation to try to prevent it. Similar to how heavy smokers often compile a list of anecdotes about the guy who lived to be 100 smoking two packs a day. That way they don't feel the need to quit - and don't feel guilty about continuing to smoke.
A second is party loyalty. For whatever reason climate change denial has become a right wing "thing." I think this goes back to the 1960's, when the environmental movement started, and the right wing came out strongly against it - because environmentalism was harming profits on some of the GOP's largest donors, like tobacco, coal and chemical companies.
A third is a bit of an anti-science thing. Many people (especially Trump supporters) see science as a tool used by arrogant elitists to claim that they are smarter than someone else. Scientists use science to say "the Earth is round" or "vaccines prevent disease" or "the climate is warming" and 'regular' people feel that they should be able to say the opposite and be taken just as seriously, because they are just as wise and important as scientists. Telling them "no, the science really is right" robs them of power. So they object to it.
Lastly there are people who simply like to be contrarians. They like to claim that 9/11 was an inside job or that the Moon landing didn't happen. Sometimes they actually believe that. Often they enjoy the attention they get when they say something that goes against science. They then are able to feel that they are special; that they share a special insider knowledge that all the "sheeple" do not.
Sometimes you see all of them at work at once, but more often people will glom onto one or two and go from there.