Why does it matter whether people believe in the alleged climate crisis?
This may seem an odd question, but bear with it for a few lines. Whether or not people in the US believe in it, and endorse doing something about it, its surely obvious now that nations accounting for at least 75% of global emissions do not. And its even more obvious that they have no intention of reducing their emissions. You want evidence? How many have updated their targets with real plans and commitments? Hardly any. As for the US, well, Trump got elected, and nothing he has done on energy policy should surprise anyone who listened to his campaign rhetoric. People in the US don't believe in it either, outside a small circle of the political establishment and media. And do they really believe? Or do they just find it politic to claim they do?.
We have to consider the curious fact that everything the climate advocates argue for doing in the US is either impossible or ineffective. An example of the impossible is NY State's intention of moving to net zero in power generation by installing lots of currently non-existent Dispatchable Emission-Free Resources (DEFRs). An example of the ineffective is California's drive to electrify transport by mandating EVs. The first will not happen because its impossible. The second may be possible but will have no effect on national, let alone global, emissions.
An interesting conclusion on this matter has been reached by a visiting group of anthropologists from Alpha Centauri who have been documenting and analyzing human culture. I have been fortunate enough to obtain a copy of the sections of their draft report covering the climate movement. It points out that the US has a strong Calvinist streak from its original founders. One of the main tenets of Calvinism is justification by faith.
It proposes to reconcile the apparent mass of contradictions in the movement by the hypothesis that the demands for belief and for ineffective or impossible actions do not in fact have any motive to produce any actions which the movement's beliefs would seem to imply are necessary. It proposes that in fact people publicly express their beliefs in the crisis and the proposed irrational remedies as testimonies of faith, marks of Grace, as Jonathan Edwards would have put it. By witnessing in this way, you can persuade your fellows that you are among the probably elect, worthy of respect, and these sentiments will be most useful in your business and social life.
You are not justified by lowering emissions. You are justified by your faith in the crisis and by your faith that DEFRs and EVs are important and valid solutions. Whether they are or not, who cares? Its faith that justifies.
Will the windmills actually produce any usable electricity? Will the EVs lower emissions? Does China show any signs of reducing its emissions? Only denialists will ask such questions, and we manifest our marks of Grace by denouncing any who ask them.
So to answer the question this post began with, yes it does matter if people believe, but not for the reasons you might assume. It matters to them and their associates because its the basis for inclusion or exclusion. It does not matter to the planet one way or the other, because these beliefs they claim to have don't connect to any transmission mechanism for effective action. In fact, if you claim to be a believer, the more extreme and impossible your demands are, the better. It reduces the chance that people will actually implement them, and that you will have to justify the results. And it shows that you are a fully committed member of the elect and so most worthy of social esteem.
Puritanism is having a long second life. The Cheka becomes the KGB, the SD becomes the Stasi. Well, that's how it looks to the anthropologists from Alpha Centauri. From what I understand, they seem to be submitting their paper to peer review here on Earth. Despite having been cautioned that if they are right, it will be a long time in review, and is unlikely to be approved. If the forces they allege are really present, they will make publication of such theories almost impossible. There will be a lot of social currency to be won from denouncing them.