Hyuuga is someone who was born with Byakugan. Kaguya's past have yet to revealed. So we cant sure if she was born with byakugan or gained it by eating fruit..
Byakugan is in her natural eye sockets, whilst sharingan/rinegan is on her forehead. Further more, the juubi doesn't seem to be connected to the Byakugan in any shape of form, so it's unlikely Byakugan stems from it.
My guess, as bizarre as it may seem, is that Kaguya from the moon, and she left her people and came to earth for the fruit. It wouldn't surprise me, seeing as how Kaguya is probably not even human. in this case, the Byakugan would be something of a celestial dojutsu that the moon people are born with. And that's why it looks like the moon itself.