Rather than age differential, I think that view is primarily founded in the belief that the President's implied power over the career of their employee (a White House intern) makes it a particularly difficult choice to risk the ire of the President by refusing their advances.

I don't get the impression from talking with younger Democratic voters that they would generally be as concerned with issues of consent if it was a 22 year-old sex worker (where it's purely a transactional relationship) or 22-year old pop star (where their career isn't particularly threatened by the President's favor).

With a White House intern, there's a potential element of silent or implied coercion which puts into question whether enthusiastic consent was freely given. Similar to the national security risk - regardless if it was/wasn't, it also calls into question the President's judgment for why they would engage in such morally ambiguous behavior - it would also be fairly difficult for the President to even know themselves whether the intern is feeling coerced or not.