Here's a very interesting article by Defending Utah about the risks involved when Utahn parents decline to vaccinate their children.
We each have a natural right to make such decisions about our respective children, and the state should not only respect our parental rights but even help defend those rights---although, at present, it violates those rights by requiring us all to vaccinate our children unless we can persuade it to exempt us for one of three reasons. Such rights-violating laws should generally be humored while we try to peacefully correct them---and so, until this law is corrected, we can either submit a signed statement exempting our children (as described in this article), or we can sign Utah's official exemption form.
Signing Utah's official exemption form is more convenient, but it is also more risky because such a signed form can potentially constitute self-incrimination if/when state child-protective-services agents ever decide (on the grounds of alleged negligence) to reassign our non-vaccinated children to another guardian that the state likes better. Sadly, family courts nationwide typically presume parents guilty until proven innocent, never involve juries, and often deprive parents of their parental rights without anything like due-process.