Schools require vaccinations to allow kids to attend. Some countries require certain vaccinations before you are allowed to enter. Stores require shirts and shoes for entry and service. Even freaking nudist colonies require you to carry a towel to sit on when you are on their properties.
I don't get the angst. You can provide proof of vaccination or proof of a negative test. Or don't go. Your choice.
Constantly complaining about "medical records" - nobody is saying you have to fork over your SSN and complete medical records. All you have to show is proof of vaccination or a negative test to walk in a door. You aren't giving them your DNA, blood, and urine samples. Nobody is seeing or keeping your private data. Get a grip.
Do you feel the same way about providing proof of vaccinations before sending kids to school as well? That's all this is.