My parents are on board with my plans. My dad had a hard time understanding exactly what it was I wated to do, but he's come around this year. I don't know what changed exactly, I just had to keep explaining that I wanted to be a professor and finally something clicked in his head. My mom has always been my biggest fan.
I think it's important to find emotional support outside your family, though, because a field as esoteric as this one offers weird emotional blows constantly. Having supportive professors mentoring me has made a huge difference for my emotional well-being.