Be careful, as Squirrels often carry hunta virus and plague.
A Canadian public-health Web site says although deer mice are the primary carrier of hantavirus, "all rodents including squirrels, rats, chipmunks and other kinds of mice should be treated as if they might carry the virus."
They don't have any particular protocols around working with local gray squirrels, so I interpret that to mean that there is little risk. There were only 243 cases of bubonic plague globally in 2018. According to the CDC, there are no known cases of hantavirus from squirrels. The only rodent species that have been seen to harbor it are deer mouse, white-footed mouse, rice rat, and cotton rat. (Neither of the latter are rat species you are likely to encounter, which are Norway and roof rats.)
"<common cute urban animal> causes <horrific thing>" is a very pervasive meme because it combines a familiar thing we're drawn to with a high risk negative outcome. That means the meme will spread dramatically out of proportion with its actual likelihood.