no, we have not seen her parents.
For some reason I keep imagining Nagatoro as Hispanic, could be her dark skin, don't know its a mystery
I have this scene in my head where Senpai goes to Nagators house to meet the parents over dinner.
The mother is a big overly friendly Mexican women who tries to give senpai huge amounts of food while telling him he's too skinny and needs to fatten up.
The father is overly protective of his daughter and gives senpai the eye while he cleans his shotgun.
This will probably happen in the American live action adaptation screen-cap this