The author's apparent disinterest in even figuring out what those exemptions (which do not exist in all states) are supposed to mean is disturbing. A basic level of curiosity surely would have prompted most people to at least "ask Mr Google" about the terms.
There are "legitimate" religious and philosophical stances that prohibit vaccinations (or certain ones). By "legitimate," I mean stances that will seem entirely non-optional to the adherents. If you really, truly believe that getting a vaccination means "burning in Hell for eternity," then you have a "legitimate", Constitutionally protected religious reason to opt-out. We don't want people to be motivated to tell lies (how else can we quarrantine the unvaccinated?) or to commit suicide (which some Jehovah's Witnesses think is preferable to a blood transfusion).
The widespread abuse of these rules is an avoidable tragedy. We just need to change the incentives to make a lack of vaccination less desirable.
For example, I'd be perfectly willing to require people that claim a "religious or philosophical" exemption to provide a notarized letter from a member of their clergy that specifically names the child, the 'unacceptable' vaccinations, explains their religious law, and says that this law would apply even if the vaccines were conclusively proven to be entirely harmless to the recipients and even if the lack of the vaccine would result in a slow, painful, and certain death for the child. This would eliminate the "well, I read scary stuff on the internet" class of fake "religious and philosophical exemptions."
I'd also be perfectly willing to make these people civilly liable for wrongful death (and lesser charges) in the event that they or their children contract and spread the disease to any person at all. There's nothing like a good old million-dollar judgment for negligence to make certain people sit up and pay attention.