You put it exactly right - she's been brainwashed by religious nonsense and bigotry her whole life, like so many people of the world. There's no bigger form of child endangerment than being anti-vax, and this person should be reported to child protective services. She is a real danger to your kid.
I would not let my child anywhere near such a mentally ill person. She won't believe she's mentally ill, and probably will never get the help she sorely needs - but you can protect your own kid and show him that there are good people who trust science and want their kids to be healthy and well vaccinated.
I hope you will go out of your way to avoid this other family. Just the very childishly stupid belief that "cavemen never existed" would be enough to drive me away from this incredibly screwed up person and never want to have any affiliation with them ever again.