Hmm, I don't think it's a matter of bowing down before anything, though.
I can only speak for myself of course, but from what I can see nobody is claiming that modern mainstream medicine always gets it right and never produces adverse results. Or that there are no problems it cannot solve and that all the doctors and nurses practising it have passed an official no idiocy test before receiving perfect training.
In my view what matters is the acceptance of the idea that medicine (and science in general IMO) should be evidence based. The demand that claims be backed up with something more than assertions that "it works".
Some ideas may simply be crazy. If a person honestly believes that 2+2=5 "just feel right" this may not have much of an impact on the rest of us. In other instances though, people's insistence on their special woo can range from extremely selfish to downright dangerous.
One of my all time favourites in this respect is the whole anti vaccines thing: so you're basically refusing to vaccinate your children because of potential adverse effects? At the same time you're relying on them not getting polio because almost everybody else has vaccinated their own children against it and it therefore not being something they cold catch in many places.
This is only not unethical if you'd do the same thing in a country where polio occurrence is actually high, i.e. if you think polio itself is less risky than the vaccine. Otherwise it's simply cynical exploitation of the fact that other people's children shoulder the supposed risk for yours too.