Well, it was supported by a personage like Oliver Wendell Holmes. I will quote, and then add my own emphasis:
"We have seen more than once that the public welfare may call upon the best citizens for their lives. It would be strange if it could not call upon those who already sap the strength of the State for these lesser sacrifices, often not felt to be such by those concerned, to prevent our being swamped with incompetence. It is better for all the world, if instead of waiting to execute degenerate offspring for crime, or to let them starve for their imbecility, society can prevent those who are manifestly unfit from continuing their kind. The principle that sustains compulsory vaccination is broad enough to cover cutting the Fallopian tubes."
Let me repeat: The principle that sustains compulsory vaccination is broad enough to cover cutting the Fallopian tubes. From the Supreme Court, no less. You can read about Buck v. Bell on your own time, but even in 1978 that sort of thing was rippling down to a minor being sterilized without her consent and the judge responsible prancing away scot-free (Stump v. Sparkman).
Any vaccine mandate needs to come with a hell of a lot of fences (thou shalt not change vaccines) and traps (if you try to extend this past vaccines we cut off your head on the steps of the White House). It needs to be surrounded by thou-shalt-nots to avoid the kinds of overreach that are actual matters of historical record.