"Condition two is that I'm pledging to take as an enemy whoever actually did kill Narcissa, as determined to the honest best of my ability as a rationalist. Whether that's Dumbledore, or someone else. ...

... Condition five is that if whoever killed Narcissa was tricked somehow into doing it, then my enemy is whoever tricked them, not the person who was tricked."

And yes, I think it would be somewhat difficult on Harry's part to explain himself to the people who care about the person who did it; but in this case, Hermione of all people would probably understand why Harry took as his enemy someone who - again - burned an innocent woman to death. I don't think that's the kind of thing Hermione would be willing to let slide just because the person is a friend's aunt.