Avirah, actually it is in the toichacha that a large number of Jews will fall away.
I’m not saying to do away the kiruv movement in Israel where the majority of people who say that they are Jewish are truly Jewish (at this time) . I am talking specifically of kiruv in the US.
It is absolutely not the duty of frum Jews to place their own and their family’s ruchnius and children’s education at second place to make find people who SAY that their grandmother was Jewish and even spoke a word or two of Yiddish. That is no guarantee that they are Jewish.