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Yes, the military member could get into trouble. This is because the Uniform Code of Military Justice has its own age of consent (16), which doesn't rely on a state's age of consent UNLESS the state's age of consent is actually more restrictive.
So, if a state has a rule allowing 15 year old age of consent, with the parents approval, that wouldn't change the military rule of 16 being the lowest appropriate age of consent.
However, if a state has a rule making 18 the age of consent, then that higher (more restrictive age of consent) applies.
So, if the enlisted member's command has an issue with this relationship, they could legally issue a "no contact" order just for dating AND any sexual activity would be a violation of the UCMJ.
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