This story is problematic af under the wholesome dressing. There was absolutely no reason that they needed to be cousins. Just being childhood friends would have functioned the same, and would have removed the ick factor. And is Nao not creeped out by the level of surveillance Monjirou places on him?
He literally flew halfway across the world to check up on him for a fever, which he only happened to find out about because he watches him on security cameras 24/7.