This is one of the many reasons that "parental rights" people are dead wrong. People as young as 12 should have the absolute right to seek and get, in confidence, this vaccine and other health care. Nobody should give any weight to whether their parents want them to not have this vaccine.
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(In fact, parents' rights to consent to underage marriage in some states is currently a loophole in this regard. https://www.mcgill.ca/newsroom/channels/news/child-marriages...)
> In many U.S. states, children can legally marry at an earlier age than they can consent to sex, leading to situations where sex between spouses may be a criminal act. Some states exempt sex between married spouses from their definition of statutory rape, which may create perverse incentives for child marriage, according to researchers from McGill University.