The largest demographic differences among major subgroups are by race, with nonwhites much more likely than whites to say they would like to see their son or daughter go into politics. This is not a reaction to the fact that the current president is black, as Gallup has found that same racial difference when the question was asked in the 1990s when George H.W. Bush and Bill Clinton were president.
The racial differences may be behind the slight tendency for Democrats to favor a political career for their sons and daughters more than Republicans do, with a larger party difference for daughters. There are also small, but not necessarily meaningful, differences by gender and being a parent of a young child.