Presumably, a law mandating the vaccine would not carry a a provision requiring parents to change pediatricians. So any "sex education lectures" that might violate these parents' innocent little darlings' "youthful innocence" wouldn't be changing due to the vaccine mandate. No one is completely safe from rape, and even the most hard-core fundamentalist versions of Christianity allow for forgiveness of sexual "sins", so a young woman who has perfectly virtuous in her religious parents' eyes may still marry a man who has been sexually active before marriage (or for that matter, who is a widower and whose late wife was not a practitioner of lifelong monogamy), and be exposed to HPV. Parents who want to reduce their children's risk of cancer will want them to have this vaccine (and it is presumed to also be preventive of penile cancer, which, though much rarer than cervical cancer, is nearly always caused by the same strains of HPV). Whether this vaccine should be mandatory or not is an issue of political philosophy (i.e. should the government be able to mandate anything?).
As for the money thing, no state or federal government should be mandating anything that is provided by only one seller. I'm not sure how to get around this while still protecting the intellectual property rights of the seller, but there must be a way. If some private company develops a highly effective vaccine for a disease which is a critical public health/national security issue, mandating the vaccine would probably be an appropriate role for government (especially if it carried an informed opt-out provision), but neither mandating huge profits for a single company, nor mandating confiscating that company's valuable intellectual property rights would be appropriate. We'd better figure this one out before al-Qaeda starts deliberatly spreading something like Ebola or SARS or some new bug they've cooked up.
Glaxo Smith Kline is currently in late stage clinical trials for it's HPV vaccine so there will be competition soon.
Read about "Reardon Metal".
I would reword your first line:
No state or federal government should be mandating anything that is not stipulated in The Constitution.