I like History, not that keen on Hollywood history, faction, I would rather they stick to the story or just go with something obviously not related.
I am not familiar with Barbie at all, I know of Ken so would have no reason to notice any issues with the Barbie lore assuming there is one so Barbie all the way.
Interesting fact, when they first produced Barbie dolls they were made in Japan and the samples had nipples and one of the guys involved was tasked with removing them and sending the samples back. Happened a few times before they got the idea.