Two doses of MMR in childhood is considered 97% effective; one dose is 93% effective. However, immunity DOES wane with time and for those with heavy exposure--including travel and work in health care, a booster dose as frequently as every 15 years may be necessary. And even 3-6% receiving who do not mount a fully protective immune response is a lot if there is significant virus circulating--especially given this is the most infectious virus we deal with.
Then there is the specific case for a subset of older people born before 1963 who may have had inadequate immunity if they received two doses of INACTIVATED vaccine, rather than modified live virus as used subsequently (and which the jackass, RFK JR wants to pull, despite his endlessly and intensively discounted claims of an association with autism).
"Cold chain"/ Storing/Holding Temperatures:
While most facilities, clinics, and hospitals take great pains to ensure that they store and hold vaccines at the proper temperatures, this may increasingly need to be looked at. Merck's NEW MMR-II vaccine has more flexible storage temps after reconstitution (i.e., powdered product added to diluent sterile liquid) and can be refrigerated (36-46F) OUT OF LIGHT for up to 8 hours, but not frozen. The problem comes when it sits out at room temperature after reconstituting for hours in direct light--something not all that uncommonly seen at busy clinics.
Other brands of MMR vaccines have even stricter handling and storage requirements.
For all those reasons, it is possible that some of the "breakthrough infections" in seemingly fully vaccinated people, especially children, may be from a partially inactive vaccine resulting from handling and storage issues. One would hope this is a rare phenomenon, but not one I'm aware of receiving recent investigation.