Board Thread:Naruto: The Last Discussion/@comment-732150-20150205151208/@comment-945885-20150206044412

The most obvious explanation is that Hamura had human descendants who remained on Earth and lost the Otsutsuki name (say, a daughter who married into another clan). The Hyuga are Hamura's direct descendents, after all.

When considering the other bloodlines and traditions that date back to the Otsutsuki Clan, you also need to keep in mind that Kaguya, Hagoromo, and Hamura weren't the only members of the clan. There were cousins, aunts and uncles, etc.

If the databook is any indication, there were other clans beside the Hyuga who inherited the byakugan, but over time it became increasingly rare. The Hyuga were unique in recognizing that and took steps to preserve the dojutsu, hence the two branches of the clan that allows safe marriage and procreation between distant cousins. The trait is seemingly so recessive that even Naruto and Hinata's children didn't inherit it.

As for the Byakugan predating chakra (which I believe is the case?) -- another strong possibility is that it's how they found the chakra fruit in the first place. They were on a voyage seeking the Divine Tree, so it makes sense to me. Maybe there's a much deeper backstory there about the world they came from.