Final answer:
The MMR vaccine must be postponed due to the recent immune globulin injection, not the past thrombocytopenia or mild fever. The claim linking the vaccine to autism is false, and delaying vaccination poses risks of disease outbreak.
Step-by-step explanation:
The nurse should tell the child's parents that the MMR vaccine must be postponed for a period after receiving an immune globulin injection. While a previous history of thrombocytopenia that has resolved does not contraindicate vaccination, the main concern is the administration of the vaccine so soon after the immune globulin. Immune globulin can interfere with the vaccine's efficacy.
Regarding the child's current mild upper respiratory infection and low-grade fever (100°F), these are not contraindications to vaccination. A mild illness is generally not a reason to delay vaccination. Although parents may come across information suggesting that the MMR vaccine is linked to autism, this claim has been thoroughly discredited in scientific studies. It's also important to remember that diseases like measles, mumps, and rubella have not been eradicated and can still pose a risk to unvaccinated individuals, potentially leading to outbreaks.