Well, there's a lot of things we do now that aren't natural. Ever take an antibotic for strep throat? Not natural.
I actually agree with the theory of vaccinations. There are a few illnesses where being vaccinated has been proven effective and have eradicated many deadly diseases: small pox, polio to name two.
That said, I do think that vaccines come with side effects. Some of them very, very serious. And while those reactions are rare when you think about how many people are given a vaccine versus how many people have a serious reaction, it's easy to dismiss them. However, I'm sure that the people who do have reactions aren't feeling like it's all that rare.
There are many people who have experienced sensitivities to previous vaccines, or they have experienced sensitivities to medications are chemicals such as perfumes, cleaning supplies, etc. I think those people have every right to be cautious about taking a vaccine and they should be able to look at their own medical history and make that decision.
I, personally, am not comfortable dealing with 3 weeks of side effects from a vaccine so I balance the risk of the illness against the symptoms I might very well experience. The flu shot is one that I forgo because I actually kind of believe it is overhyped and I'm not 100% convinced that it does a good job from season to season and there's really no way to know for sure if it worked in any given year or it didn't.
If the OP has valid concerns about a reaction in her child, I think that should be respected. Since it is the law in NJ to get the vaccine, it would seem to me that she could discuss those concerns with her physician and the physician would have the ability to waive the requirement.