The great benefits of vaccines, which include that they have saved millions of lives, far outweigh any small risks.
The Leicester Method of dealing with smallpox does not support the idea that smallpox was eradicated solely with good sanitation and quarantine folks with smallpox. They used vaccines too.
We might have to worry about even larger outbreaks of measles and other vaccine-preventable diseases, but it won’t be immigrants and refugees causing them. It will be because more folks are skipping out on getting vaccinated and protected.