I mostly grew up with my single father, who has always been fiscally and socially moderate Republican. The first time he voted, he voted for Eisenhower's second term as president.
When I was a kid, I didn't follow politics much and figured I was the same, a moderate, and someone who should register as a Republican. I quickly realized how liberal I was when I did research in my late teens, though. So I guess it could be said that I quickly moved in the liberal direction when I became involved in politics to any extent.
My father in the last few years became more liberal in his seventies. According to him, he hadn't changed much at all, but just realized how far to the right everything shifted, so that his moderate views were now considered Democrat, or left of Democrat. He voted for Obama in his second term, and other Democrats, and didn't view them as quite liberal enough either. He was for progressive taxation, government support of healthcare, government support of education, gay rights, women's rights, freedom of speech and religion, protection of the environment, legalization of marijuana, staying out of most wars, etc. He became pretty vocal about it, and debated his son a lot as well, because he was more liberal than his son who works to produce weapons.