My best friend is an INFJ, her family was very P-ish. Her mom is super duper emotional and wishy washy and her dad was a pandhandling musician. Not a lot of stability. She's super duper rigid and efficient. Very rules/organized driven.
I am an INFP, my mother I believe possibly is an ISTJ she was very detached from us, but we were clean and fed and things were always in order. My dad was extremely comntrolling and abusive. I remember never playing with my toys because my mom would freak if the room got messed up. I would just sit and long to play with the dusty little creatures on the shelf.
I don't know how that all effects personality, but I'm sure there is some overlap between genetics and environment.