To my knowledge, cervical dysplasia is not genetic. It is a caused by a specific type of HPV which is sexualy transmited. There are many types of Hpv's. Cervical dysplasia, the way I understand it, is an "infected cell" that may or may not cause problems depending on your immune system and depending on what hpv type one would carry/have.
I can go on,,,if you'd like, but this is how I would sumarise it.