Sakura didn’t want to tell Sarada about her awakened Sharingan when she was little
and when she was old enough to realize it she forbade her from using it
Yet Himawari is fully aware of hers at such a young age
and when she’s older she’ll likely be able to train with it with either her auntie or mother.
even though Hinata herself was kidnapped as a child for her byakugan and it’s likely still a very precious and sought after dojutsu to this day.
So Hinata and Naruto are either confident that no one will find out about Himawari’s byakugan or no one would be brave enough to mess with one of their cubs.
And another thing:
They don’t live at the Hyuga compound and if you look at their house, you’d never guess that any other Hyuga lived there besides Hinata
and she nor Himawari wear the Hyuga crest
Then we have Sakura’s house and clothes:
If she doesn’t want her child to become a kidnap victim for her dojutsu she certainly has a funny way of showing it
Cheloneuniverse 