Poli sci people are very proud of their studies showing that greatest political socialization impact of family is on party identification: children tend to choose same one as their parents (when parental partisanship differs, children identify more often with mother).
Much of this research was conducted several decades ago and more recent studies indicate that parental influence on children is not as strong today as in past on attitudes about political/social issues.
Re. latter point, polic sci mainstream pines for stereotypical/mythical two-parent family that sits down together at dinner table and talks about "issues of the day." Michael Hoover