The title should be relatively self-explanatory. Do mature minors (aged 16 or older) have a legal right to privately consult with a medical professional, free from the involvement of a parent, guardian, or some other individual in loco parentis?
If there exists any applicable state law, Minnesota is my area of concern.
The answer from User6726 is true, but it leaves out some things. The minor may consent to medical treatment if he/she is living apart from the parents and managing his/her own finances. (Minn. Stat. § 144.341)
The full list of things a minor can consent to aside from that, are as follows:
to determine the presence of or to treat pregnancy and conditions associated with pregnancy
for sexually transmitted infections
for alcohol or other drug abuse (Minn. Stat. § 144.343, subd. 1)
hepatitis B vaccinations (Minn. Stat. § 144.3441) and
blood donation (only those 17 and over; a 16-year-old can donate with written consent from a parent or guardian) (Minn. Stat. § 145.41).
Health services may be provided to minors without the consent of a parent if, in the health professional’s judgment, treatment should be given without delay, and if obtaining consent would result in delay or denial of treatment
That list and a few other items can be found here: https://www.house.leg.state.mn.us/hrd/pubs/ss/ssminorhc.pdf
If the minor is legally able to consent to the treatment, the parents do not have any rights to the minor's treatment. The Consent of Minors for Health Services says when that is the case – living apart, married, have given birth, also for diagnosing pregnancy, substance abuse, "veneral disease", Hep-B vaccination (there is an abortion-related counter-command). If, for example, a minor wanted to be examined for a sprained ankle, that is not covered by the various minor-consent laws, so a parent/guardian would have to give consent, and would be entitled to be present during the consultation.
