Here is one study, it is fairly typical of the kind. (I can gladly dig up more for you, but this is one of the better ones.) It finds family effects, but they are much smaller than many people would expect. Of course it is more difficult to find out whether a child is "rational" as opposed to intelligent, and the same is true for parents, so there are no data (to my knowledge) on how much parenting affects scientific inquisitiveness.