Yeah, I think this woman's (and her legal team's) issue is that she says her religious beliefs are against vaccination, AND she identifies as a devout Roman Catholic.
Don't get me wrong, Catholics definitely can disagree on things (if you're feeling little-t trollish, go onto a Catholic forum and start a "Mass in English" vs. "Mass in Latin" debate sometime).
But for better or for worse, the local diocese, and the archbishop in charge of it, gets the final word. That's just how the Church works. Don't like it, there's the door.
So, it doesn't look too good for this woman when she's saying "I can't have my kids vaccinated because I'm Catholic", and there's an entire huge diocese, with many Catholic schools in it, right next to her, saying, "Um, that's actually not so..."
ETA: Oh look! Here's FidelisCare, the NY State Catholic health plan, "urging parents to ensure that their children's vaccinations are up-to-date", as of April 2012... http://www.fideliscare.org/news/index.aspx?view=art&cid=0&aid=3363&parent=3363
Edited by glassesgirlnj - 2/17/13 at 7:40am