Those vaccines and diseases have been around for decades so the disease itself and vaccine delivery method is well understood.

The two most effective COVID-19 vaccines are based on newer technology that has never been mass produced or widely deployed or gone through the full approval process. In the US, they are still considered "emergency use only." As such, a larger segment of the population is skeptical/hesitant of the vaccine. They aren't anti-vax or anti-science, they just want to see more long term data on the vaccine and even COVID-19 before they get the vaccine.

Additionally, it's been suggested the usage of the vaccination records wouldn't just be to go to school but to do routine day to day things, like going to concerts.