I agree with basically everything you've said but I'd caution that "broad support for doing something" without much care as to what is a recipe for a lot of bad things to come to pass under the guise of fighting climate change.
Of course, I'm only challenging the notion that there is complete ignorance about the need for action. What that action looks like is up to us. I would say we are actually already on the path for "a lot of bad things to come to pass under the guise of fighting climate change." It is the explanation for a lot of the trends we are seeing like nationalism, the strengthening of borders, and the weakening of labor representation.
If that's truly your fear, you should support real (and acceptable) moves for fighting climate change as a way to head that off at the pass before it comes to be.
Today, if you make a list of all the fascistic bad things that governments have done "under the guise of fighting climate change" I'm pretty sure the set is empty, it's a zero item list. No government anywhere is a green fascist dictatorship, and it seems far-fetched to imagine one. But again, if you think that's a real risk, I urge you to support climate action now so that public support for drastic action doesn't build up.
You appear to be reading a ton of sentiment that isn't there into my comment. All I'm saying is that opportunities for big action give cover to those looking to do bad things that would not otherwise be acceptable and give cover for people who would not otherwise condone those bad things to ignore it. We need to be vigilant so that we don't say we're fighting climate change but instead wind up off in the weeds screwing over people.
And for the record, I am strongly in support of any progressive (as opposed to regressive) measure that has a net positive impact on climate change.