Why can't people with tattoos be buried in a Jewish cemetery?
There is no such rule.
It is true that Jews are prohibited from getting tattoos under Jewish law; the rule in question is in Leviticus 19:28. With that said, violating this law does not disqualify one from burial in a Jewish cemetery.
While this alleged rule was a central plot point in a 1996 episode of The Nanny, it is a complete myth, of unknown origin. But you don't have to take our word for it. Here are opinions by an Orthodox rabbi and a Conservative rabbi.