Not a question of minors, but of people in positions of authority and people in very much junior positions. (And you can't have a much more extreme example of that than a President and an intern.) The ground rule is that they need to negotiate things, and the personal relationship can't be allowed to progress very far before a change in the working relationship is required.

It's not unlike the situation where a doctor and a patient are attracted to each other. It has to go on hold until the patient is no longer a patient of that doctor.

Conservatives have stricter rules about these things? Not in England under Thatcher, that's for sure!