The average person isn't so blind they don't see the changes. The frog-boiling experiment is a myth. When there are state-spanning fires that darken the sky across the whole country every year, and hurricanes strong enough to shut down city infrastructure are a regular occurrence, and crops fail and lakes run dry and insects that were so thick twenty years ago you couldn't see through them can no longer be found, people notice. I think these things add up to much more psychological damage than the abstract fear of missiles, even if most don't connect it to climate change directly.