I have not seen any evidence of a "large percentage of the population becoming useless" due to fear of climate change.
Can you provide a citation?
I have seen people with a basic background concern about climate change, and some people have more of it than others, but I don't see a "large percentage" of people becoming useless.
People have lots of fears. Some even more more pressing than climate change. Human beings are able to handle and process many different fears of varying intensities simultaneously, and have for thousands of years.
I have also not seen any information that the psychological fear of climate change is worse than actual climate change. One provokes level of fear in a subset of the population. The other will kill us all.
Perhaps the best way to fix those psychological fears in people is to fix the climate so they don't have to worry about it?