It is an obligation to listen to the doctors (Maharik Shoresh 159, Shevut Yaakov 1:65, Yalkut Yosef Kitzor Shulchan Aruch Laws of the Doctor and the Obligation to be Cured 2). As this is a public health matter it would seem that he authorities should compel parents to vaccinate their kids.If they do not are their kids become ill they would chayavim b’dinei Shemayim (as it is gramma).
Once a baal bayit refused to eat on Yom Kippur against his doctor’s orders. He died and Rav Yaakov Kaminetzky, who was the rav of the town, ordered him treated like a suicide.