In my experience, cricket is definately a dynastic sport. I come from a minor Essex cricketing dynasty, and I know most, if not all, of my club side in Devon had parents or grandparents that played, mostly in Devon. I think that cricket fans are born. If you spend hours as a kid around cricket with your family, you are bound to associate it with good things, regardless of your own ability. With regard to ability, it is certainly genetic, with good coordination, reflexes and eyes being inherited characteristics. Unfortunately for me, I inherited all of the (nurtured) love of cricket and none of the (natural) ability!
I also think that you are more likely to enjoy cricket if you come from a non-cricketing family if you went to public school, because they have the (compulsory?) opportunity to play, away from the club system, which tends to be a familial thing.