I think the ideal thing to add some sort of safety net when you change parent permissions to ensure there is no case where and child subcategory is less restrictive than parent. Add that same safety net when saving a child category.
The worst case is when you can not access a parent but have access to a child. Stuff simply does not work right.
I think simply raising errors for now when you try to save in such conditions is the best path forward.
Eg:
Parent:
Staff: read
Child:
Team: read
(click save on child)
Users in child category will not have access to parent category, save is not allowed!