That HPV vax is terrifying. I had it pushed on me like crazy because any time I was tested for HPV it came back negative (which apparently is "impossible" and they'd retest me, until I just stopped going to gyno appointments). "Oh, here's the HPV vax since you are negative, it will keep you negative". Uhm. No. I'm negative because I don't sleep around. Geez.
Wise wise decision to reject that shit. As soon as they came up with the hpv vax I told people to stay away from it because hpv is generally spread through lots of casual sex with multiple partners.
Babies don't need it, little girls and boys don't need it. Sexually continent, healthy men and women don't need it.
Unfortunately babies can get it from their mother's birth canal if she has an active infection- bad news.