There's a strong little community within the homeschool community that eschews conventional information because it doesn't make sense and doesn't conform to expectations, personal experience, or anecdotal stories. Evidence from a peer review journal will never convince them certain events were coincidental and not causal. It's not just homeschoolers, btw, but ignorance of what the scientific method really is, what it does, and the value of rational, evidence-based critical thinking.
While I agree with the general point, I can't help having a certain degree of sympathy.
In a blast from the past, here is what I said in my very first post on the original WWGHA forum, all the way back in December 2006.....(it was actually in response to a point someone had made along the lines of "I know Christianity is bunk, but I sometimes still worry about hell")
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In the UK, we have a vaccine called the MMR, which has been "linked" with giving children autism. One doctor looked at 12 children whose parents had basically asked him "prove a link". He also had been working on a new vaccine that would have made him a fortune had the MMR been discredited. Most stories were along the lines of "my baby was fine - but then 8 months (or 5 months, or 12 months) after getting his MMR he became autistic". The tabloid press worked the story up. Vaccination rates dropped to levels where they might be a measles epidemic. However, if you actually LOOKED, there was no credible evidence of any link whatsoever - just interested parties, hysteria, and fear.
And then it came time to have my little girl vaccinated. She means the absolute world to me. My brain was 100% certain it was safe to give her the MMR.
But I was still afraid. As I said to the doctor - "my head is convinced, my gut is not". Despite being as sure as sure could be, and backed up with the evidence, I was still afraid. The months of screaming in the press, and the thought that "what if I hurt my little girl?", it all made me fear. Even the solid fact that if I did NOT vaccinate her she would have a definite (though small) chance of death, sterility, or blindness if she caught measles did not help. The baseless superstition had gotten into me and it hurt.
That's what it feels like to be raised Christian (however woolly) and then try to de-faith yourself. All the logic in the world can't silence that little voice screaming "BUT WHAT IF YOU'RE WRONG?!?".
So I wish you all the best, and promise you that the voices slowly fade.
...and I gave my daughter the vaccine. And she's fine.