The tie with Jewishness is like any other blood tie.
It cannot be changed, and a person cannot leave the Jewish family.
To be a member of a family is a fact that a person can relate to emotionally in any manner he pleases, but he cannot alter the fact or cut the tie.
He is genetically bound up with the family past, and thereby also bound to its present and future.
For the same reason, a person cannot leave or be ejected from the Jewish family.
In actuality, as in private families, a person can run away from home and try to forget his origins, or the members of a family may decide to throw out an individual who has disgraced himself.
Even if both sides were to sever all connection, whether by word of mouth or by some sort of ceremony and practical excommunication, the essential tie could not be cut.
There is no way of leaving the Children of Israel.
A Jew who assumes another religion, and in many matters ceases to have any relation at all with Judaism, is still a Jew.
There is no way, not by an individual decision nor by the authority of a social body, to take away anybody’s Jewishness.
Even the one who is excommunicated is merely being punished and set aside; he is being separated from the community and its benefits; he is not deprived of his identity as a Jew or of his Jewish religious obligations.
The same is true for those who enter the Jewish fold by conversion.
The Halakhah expresses this “family” connection by identifying the act of joining the religion with a tie to the Jewish people.
It is a family tie.
A proselyte Jew is like a newborn babe (Yevamot 27a).
The entry into Judaism is an extrication from previous biological antecedents and a rebirth as a child of the family of Israel.
–Rabbi Adin Steinsaltz