Does anybody hold that one should not vaccinate, and if so, what is the debate?
All (!) halachic authorities obligate taking medically recommended vaccinations. Judaism clearly believes in man’s Free Will and the significance of our actions, and not in pre-determinism or fatalism. We definitely are against saying: “If God wants me to be sick or healthy, that’s what will be anyway, so why take vaccinations…”! For one isn’t allowed to rely on miracles, but must follow the way of the world (e.g. Rashi, Tosfot, Bava Kama 85a). What you may have heard is that there is a place where some mistakenly (!) understand the Talmud (Brachot 60a) which says that doctors have “permission” to heal, as if to say that it’s just permission, and not an obligation. But Rashi and Tosfot already explain that this is davka to correct the possible mistake that some religions make, thinking that medicine “overturns” (sic!) the will of God (ibid). Alternatively, the Ramban (who was himself a doctor!) explained that this quote is to make sure that potential doctors don’t say, “who needs this headache- what if I might make a mistake…“, but in fact, healing is a mitzvah, and not just permission (Nedarim 41b). Similarly, there is an oft-misquoted mishna which says that the rabbis were in favor of King Chizkiah’s “discarding” the “Book of Medicines” (Psachim 4, 9), whereas the Rambam (who was also a world-class doctor!) explains that it was a book of old remedies which was being misused, killing people instead of healing them. I have heard that there is a small cult of extremist Ba’alei Tshuva who won’t vaccinate their children, but this misunderstanding is against all of the poskim and must be corrected!