Big obvious one: intermarried Jews. What to do about the spouses? Say nothing? Tell the Jew to divorce the non-Jew? Facilitate the conversion of the non-Jew?
Let’s say you’re setting up a school as a kiruv project (Chabad has created 100’s of such schools.) Do you only accept halachically Jewish kids (as a normal Orthodox school would do), or do you accept kids with only a Jewish father, in order to try to mekarev him?