Their malpractice insurance policy companies may be demanding it. ( in other words, Lawyers!)
If a doctor accepts unvaccinated children into his practice, the child who is sick with a preventable communicable disease can ( and likely will) infect other children and adults in the waiting room. Not everyone who is vaccinated responds with antibodies and even though vaccinated is completely vulnerable to the disease. Also, some children and adults have medical conditions that prevent them from being vaccinated.
Personally....I think this is good medical practice, for the safety of the others in the waiting room.
Unvaccinated kids are far less likely to get communicable diseases, because their immune systems are not crippled by the passenger virus SV40 that is present in most vaccines.