It really has nothing to do with CFR. Back in the early days of vaccination, people were generally more distrustful than today since vaccines didn't really exist before that time, so there was no frame of reference, and understanding the science behind it was (and it still can be for the average joe) hard.
In the case of TB and Polio, there were also incidents with contaminated vaccines which further eroded confidence at the time.
At this point in time though, with a track record of over 100 years, the risk/reward ratio, process, effectiveness, etc is well do ented and understood.
Even relatively-new tech like mRNA is merely an innovation on the delivery mechanism to initiate the natural reaction, there is nothing new in how the immunization process works.
Spreading FUD is the edgy thing du jour, unfortunately, and clearly has an audience.