Is it true you are a 'real' Jew ONLY if your ancestors were?

Nope, there's a difference between being of the Jewish faith and Jewish by blood. You don't have to be both to be a real Jew. I mean, Daniel Radcliffe is an atheist and he's Jewish on his mother's side. Also, a friend of mine converted to Judaism and is officially considered a Jew, but he's French by birth.