I've been thinking about this since you posted.

Legally, according to the present legal system, they do have the right to insist.

Morally, I'm not so sure they should. I don't think the impact would be lessened simply because it's a medical procedure...

I think it would depend on the child too. I definitely feel that kids who know what they're talking about and are informed should be allowed to be part of their own medical care. If they want to refuse a certain kind of treatment, etc., they should be allowed if they are well informed of all the implications.

I think I'm leaning towards the rights of the kid, but only if they know exactly what they're talking about.

I'm leaning towards the right of the adult. Some kids are smart enough to understand all of it, but some aren't. I feel the rule should be blanket to cover those kids, but flexible enough for those smart enough to have a say. So, I agree with Angel.

It's not based off a news story. More something I've come across.

The thing that really gets me here is that there are non-invasive alternatives to pelvic exams that aren't taken. I can't help but feel that unless it was essential and there were no non-invasive options (I can't think of a situation besides vaginal tearing that doesn't have a non-invasive alternative), forcing a pelvic exam on a non-consenting person is no better than rape.

Edit: I mean psychologically to the person subjected to the exam it would be damaging.

I'm definitely on the side of the child. It's THEIR body, and their right to consent or not.

Well, if they're sexually active and they decide not to get tested for diseases, then they're only risking their partner(s) health, which then they should be required to get tested. It's not the same as someone who wants to take advantage of them, which I feel like you're comparing it to.

I also feel adults should be subject to the same tests, because so many have sex without getting tested and infect others.

I'm sorry, but I got my disease because someone didn't get tested and then passed it on to me, and I was careful about condom use and who I slept with (or so I thought).

You sacrifice your personal rights when you risk someone else's health.

Until a teen is of age, legally a parent can insist on a pelvic exam. I think teens should have them done like everyone else, even if they are not sexually active they are just as likely to get cancers, etc.
At some clinics they can have it done without the parents and get results, medicines, etc. without the parents knowing. I think if a parent insists badly enough, they should be ok with bringing the teen to such a place. both privacy concerns and safety ones are addressed this way. I once had a friend who went through this, her mom was overly nosy and assumed she was having sex (even though she was not).

Although it isn't someone wanting to take advantage of them, would you deny that taking away someone's body autonomy and forcing them to undergo an invasive procedure would still be traumatic to that person?

Also, routine STD testing can be done with blood and urine testing and doesn't require a full pelvic exam.

Of further note, my opinion on this might be a little biased because I think routine pelvic exams are an outdated and unnecessary procedure as it is.

Teenager's side, for sure.

I believe if the child is old enough to refuse, they are old enough to make the decision for themselves. Pre-teens who are forced into it may have a really traumatic experience.

I was raped when I was thirteen and I never told my mother. I was supposed to get a pelvic exam and had nightmares about it for a week before I canceled the appointment, telling my mother there was no way she could force me to subject myself to something I didn't want. She took it, but didn't ask why. I'd never, ever force a child to a potentially traumatic exam if they refused.