It might be helpful to separate objections-about-vaccines, including this one, to objections to this vaccine which is seen to be pertaining to sex.
I know people have objections to vaccines - I don't happen to agree with many of them, but I know about that and to a certain extent I understand the thinking behind the objections. (To me, not wanting your daughter to have this vaccine in case she didn't then go for regular smears seems like not teaching your daughter to floss in case she then doesn't go for regular dental checkups. It's not hard to teach BOTH acts of preventative behaviour, surely? But that's only part of your objection, the rest are 'dangers of the vaccine' objections, which I can't answer to, because I don't know of any)
What I don't understand is the objections to this vaccine in particular, from a group of people who have not objected to vaccines in general, and the objections that are basically "Nooo because ...SEX!! IS WRONG!111!!!"
it seems particularly wrong to deny this vaccine to teens because it's a time-sensitive vaccine. I was about 26 when they started offering it and I'd had some sexual partners - and some broken-condom incidents. At that point there was no point me getting a vaccine - it doesn't work for people who are already sexually active. So if you deny your teenage this vaccine and they go on to have sex, as teenagers/people in their early 20s do, you have denied them the chance to be protected against 70% of the cervical-cancer causing viruses out there. It's too late for them, in their 20s or wherever, to get it themselves.
To me, it's just one more thing a parent should do to protect their child. I understand that people think their children need protecting from vaccines, but to me, vaccines are the things that protect children from diseases.
And I do not see that it is my job to attempt to prevent my (future) teenage offspring from sexual behaviour. It's my job to teach them about safe sex and consent and happiness and pleasure and emotional security. . . not to say NOOO SEX is WRONG!