The belief was one of racial superiority and hatred over the movement towards equal rights and equal access, which knocked them off the pedestal they believed they were born to be on. They didn't like how their children were being "corrupted" by the ideals of racial equality, which upset their views about social hierarchy.
Public pools shut down or were privatized after desegregation and civil rights laws made it impossible to have "whites only" public pools. There's a book on this overall topic: Contested Waters: A Social History of Swimming Pools in America.
There's an infamous picture of a motel manager pouring pool chemicals into the motel pool to scare desegregationalist activists who were swimming in it - https://rarehistoricalphotos.com/motel-manager-pouring-acid-... .
Here's background on the context of the wading pool: https://www.today.com/popculture/how-mister-rogers-pool-mome... . "This 'Mister Rogers' moment broke race barriers. It's just as powerful today / The scene aired amid racial tensions in the U.S. over segregated swimming pools, and many see it as Rogers taking a stand against racism. ... The same year it aired, the Supreme Court ruled that pools could not be segregated by race."
You can also read what Clemmons (who played the officer) has to say about it in his memoir, "Officer Clemmons: A Memoir", which has this scene on the cover.