It was universally accepted by just about everybody that Polio was a scourge.
People were terrified of it because of the awful things that it could do to you(paralysis, shriveled limbs, etc.)
People were generally not as susceptible or beholden to conspiracy theories back then, they
didn't think that the government was intentionally trying to kill you or implant microchips
in your skin to track what you did.
That being said, the "rollout" of it was rocky to say the least. There were two "competing" vaccines, the "Sabin" and the "Salk". The Sabin used "live" virus, and the Salk used inactivated virus. However, some of the "early adopters" of the Sabin vaccine ended up becoming infecting people with Polio. The Sabin was the one that was eventually settled upon, however, because it could be administered orally via a sugar cube as opposed to an injection.
I got my "sugar cube" in 1961, and had no ill effects, but there were some unfortunate people who did end up contracting polio from this vaccine. It was not without "controversy", but again at the time Polio was so feared that I think most people were willing to accept the risk of a vaccine.