Some states have significantly cut back on exemptions that aren't for valid medical reasons and home schooling isn't really a viable option for many people.
In addition, although I don't know if the case would stand up today, the Supreme Court has held that states can require vaccinations generally. (A 1905 case involving Massachusetts and smallpox vaccination.)
Fair enough, but "slippery slope" is a particularly well-known logical fallacy and it seems worth pointing out when someone invokes it as the crux of their argument. Next time I'll use better words.