let me preface my statement by clarifying i am definitely NOT anti-vax. and like the poster you are addressing, i agree that the needs of people in public education/care settings are important and it is good to require vaccination for participation.
to me, where a parent has concerns about the pace of vaccinations, a medical provider can share information with that person to help them better understand the risks and benefits of the typical schedule (as you have done). they should still have the opportunity to consent.
medical care without consent is a violation of bodily autonomy.
edit - i wonder if i was downvoted for a) i endorse vaccination as a benefit to the public, b) i think education is valuable in addressing fear or conspiratorial thinking, or c) i believe people have a right to bodily autonomy.
or was it d) i expressed these things instead of dogpiling the sovcit? 🤔