I have a question of a theoretical nature. Since I wasn't able to find much information on it, I figured I would ask.

Is it illegal for an adult to cross state lines to see a minor when the parent of the minor gives consent for the adult to be there and no sexual contact takes place?

This seems like a bit of a tricky issue, and your help would be appreciated.

No. In the scenario you gave, this would not be illegal.

What would be illegal is to transport a minor across state or jurisdictional boundaries without knowledge or consent of the parent; or, to meet with a minor in another state for the purpose of sexual contact.

A parent can not give consent to a minor or another adult to violate a state law. Parental consent will not negate the law. If state law is violated with a minor under a parents consent, the parent may also be prosecuted.