If you don't want to vaccinate your children before they enter school, some states will let you claim philosophical objections, and some will only allow you to bypass the requirement if you claim vaccination conflicts with your religious beliefs or for medical reasons. In 20 out of 28 states with medical/religious-only rules, rates of exemptions have gone up. So it's probably safe to say that some parents are lying about their religious beliefs to avoid the vaccine requirement. Now, rates of exemptions in some states that allow philosophical objections have gone up as well, and it seems to me that the more important story might be "more parents are opting out of vaccinations for kids" rather than "parents lie to get around state requirements".
Not that lying about religion is super clear-cut. The religions that oppose shots--Christian Scientists and some fundamentalists--oppose many other medical treatments as well, treatments the non-religious might want their child to have if he or she falls off the play structure or has an allergic reaction to a food, for example. I doubt most schools would run to the vaccination forms in case of emergency, especially since you don't have to state what your religion is, but personally, I'm a worrier so I think about things like that.
I get very concerned when I hear that more kids are entering schools without being vaccinated, though it's clear the numbers are still small. Babble has a good piece on this here, and we've talked about it on Strollerderby before as a social contract and a difficult choice. At the end of the day, it's a choice that can have far-reaching consequences. Part of my decision to vaccinate was this: When I worked in a public health school at a major university, I met people who led campaigns to eradicate diseases all over the world through vaccination, and the stories they told of children getting sick and dying were pretty heartbreaking. I just hope an epidemic doesn't come along to make this choice easier for parents.