Rick Perry, governor of Texas from 2000 to 2015 and then Trump's Secretary of Energy, tried in early 2007 to add vaccination against some strains of HPV that cause cervical cancer to the list of required vaccinations for children to attend public school in Texas (with exceptions easily available for parents who object on the grounds of religion or conscience), and make it free of charge to anyone not covered by insurance.

This was unpopular enough with the rest of his party that he had to give up on it. One of the main objections was that since HPV is sexually transmitted protecting against it would encourage kids to have sex.

That is of course a ridiculous objection. You'd be hard pressed to find an actual horny teen couple for whom the risk that sex would lead to cervical cancer 30 years later would be something they would consider when deciding how far to go.