I would not, not just for every one elses safety, but also I don't want to have to consider those illnesses when a child is sick, bad enough dealing with common colds, ear infections possible pink eye etc, I don't want to have to consider polio, measles, whooping cough etc, I can accept that someone wants to do their own thing, but I dont have to respect it, and by that, I don't have to include them in my business.
On a side note, I always get a chuckle when parents say " I know best for my kids" and yet we have a society full of really messed up people......not everyone knows whats best, all the time!