Barzilai and I have discussed this issue many times. Since the Torah/Old Testament mentions the importance of DNA. Why are our relatives are not called as we are into this Jewish Awakening. Sometimes one individual is called and other times whole families.
Having Jewish DNA doesn't mean a person has a Jewish heart. This article is about a man who is admitting to having some Jewish DNA, yet an enemy to Israel. Of course he says he is a Christian, Jesus was Jewish, he overlooks that.
In my opinion its about a person's relationship with G-d. A person's heart toward G-d and Israel. A person that wants to do kindness, correct behavior before G-d, out of love for G-d. Not perfection, but in G-d's mercy.
What Barzilai and I have noticed in this Jewish Awakening, you have the DNA, but must have the passion for G-d to activate the Awakening. G-d of course is in control of it all.