From everything I've learned about WIC immunizations are not a requirement. In fact, IIRC somebody here pulled the Patient Privacy Act on them regarding vaccines.
That said, a religious excemption should work fine. Just stand your ground and don't allow yourself to be bullied. Our WIC office shares space with the public health clinic, so you can imagine their attitude when we tell them we don't vax. Don't give an inch, don't act nervous. Simply state that vaccinations are against your religious beliefs.
Homesteading Mama to homeschoolin' kiddos London (10) ; Alexander (8) :; Holden (5) :; and Sergei born at home 8/18/08