I have some thoughts on this matter, let me know what you think. There are two types of reasons, one pertains to other views which interconnect in the political realm and the other is in framing.
First, the largest issue is that "climate change" is often. attached to various political causes. When someone presents something as "We need X to do Y" but they believe Y to be wrong/immoral/evil they rightly will become suspicious of what's being used to promote what they see as wrong. There are all sorts of political causes and buzzwords which get attached that send certain groups signals not to trust what's being claimed (Note [1]).
Second, the framing of the issue is often done poorly. Large impractical and unpopular efforts are put at the forefront, i.e. the recent stove controversies, instead of framing the issue around energy independence and personal safety/wellbeing. Regulations are framed in a way that primarily appeals to certain demographics, making the opposition less likely to trust root claims. There are various other examples that could be made.
These issues make it very hard for people trust root claims. When someone presents something which you deeply believe is wrong, on any number of political issues, and then in the next sentence says "oh yeah the world is coming to an end unless you vote for me" it makes complete sense, id even say it's rational, to be highly skeptical of the claims being made (though ideally someone wouldn't remain in a skeptical phase and instead would dig deeper).
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1. For example, there is often an attachment of climate change with racial grievance politics which are widely contested for independent reasons. Phrases like "climate justice" and others often inherit a certain framing which not everyone accepts. Whether you think these things are good or not isn't the issue, it's the perception which then causes distrust.