“The apple doesn’t fall far from the tree.”
Actually, with parents I often find that the child goes in the opposite direction. We have in our fair city an honest-to-G*d commie on our city council. I practically fell out of my chair when I learned that his son (with the same name) is a registered Republican!
It's rare.
There are a lot of studies which confirm that after a (typically brief) rejection phase adult children share their parents values and worldview by overwhelming majorities