Also, his father said on one episode that he voted for Kennedy. I think it would be odd that "the old man" is a democrat, and his son is a republican.
Democrat in 1960 is much different than Democrat in 2016. Different issues, different positions, et cetera. Lots of people who had a party affiliation back then have since switched, like Hillary Clinton and Rick Perry. The south was once more solid for the Democrats than it is now for the Republicans.
Kennedy was just as liberal as many Democrats today. It's a perfectly fine point.