Very little. Most countries where immigrants come from have better MMR coverage, acceptance, and trust that the communities in the US where we’re seeing outbreaks. Chickenpox is the one vaccine preventable that is rising due to immigration, because the chickenpox vaccine is not usually given outside the US.
Most cases of measles are from unvaccinated US residents traveling and bringing it back.
There was that big outbreak in the migrant shelter in Chicago. The underlying cause there was Venezuela’s collapsed healthcare system and the concentration of immigrants from there in the shelter instead of allowing for opportunities to establish themselves in uncrowded housing such as with sponsors or in separate housing.