Nothing in the Immunization Act shall preclude the right of the patient, or the patient’s parent or guardian if the patient is a minor, to claim exemption from immunization as defined in Section 24-5-3 N.M. Stat. Ann.; nor shall anything in the Immunization Act require such patient to be included in the immunization registry if the patient, or the patient’s parent or guardian if the patient is a minor, objects on any grounds, including that such registry conflicts with the religious belief of the patient, or the patient’s parent or guardian if the patient is a minor.