There are many who do "direct care", which is an alternative to the insurance-driven industry. Our doctor doesn't push the issue.

It takes some research. Some pediatricians will put it right on their page if they won't accept children that don't take the vaccines. There are lots of hippy forums online that have compiled lists, like mothering.com is a resource I used to find decent pediatricians way before the covid madness.

I'd recommend that someone just calls around, says they have religious reasons for avoiding vaccines, and see who is ok with it. Legally they put themselves in a questionable position if they refuse to treat patients that don't take certain drugs for religious reasons.

Honestly, pediatricians don't do a whole lot other than give shots to kids. They take measurements, take their weight, and give pretty basic nutrition advice. Maybe they catch that 1 in a 1000 kids that have a rare heart defect when they listen to their heart. But otherwise, most of what you need a doctor for, like occasionally getting antibiotics, csn be done through telehealth. And if it was an immediate problem, you just take them to urgent care or the emergency room anyhow.

Chiropractor or functional medicine doctor