The question was posed to Rabbi Moshe Feinstein (Russia-New York, 1895-1986) whether a Yeshiva may accept a child born to a mixed marriage, where the mother is Jewish but the father is not. According to Halacha, the child’s status in such a case follows the mother, and therefore the child is a full-fledged Jew. But is there any reason for a Yeshiva to refuse to accept such a child, or for a congregation not to allow this child to observe his Bar Mitzva in their synagogue?
Rabbi Feinstein ruled (Iggerot Moshe, O.C. 2:73) that a Yeshiva should not accept a child born to a mixed marriage, and a congregation should not agree to host the Bar Mitzva celebration of such a child. Accepting the child in the Yeshiva or hosting his Bar Mitzva celebration may easily be misconstrued as implicit approval of his parents’ lifestyle. In order to firmly establish the Torah’s strict opposition to intermarriage, Yeshivot should not accept children from mixed marriages, and synagogues should not host Bar Mitzva celebrations of such children.
Needless to say, if the mother performs Teshuva, then clearly the Yeshiva or synagogue should welcome the child, even though he had been born to a non-Jewish father. It should be noted that certain communities (for example the Syrian Sephardic Community in Brooklyn New York) are strict in all these situations no to accept.