Q. Should synagogues welcome people who have married out?
A. Before addressing your specific question, two prior axioms: We have to encourage marriage as a principle, with the commitment that it brings to each other and to the future; and we have to encourage people to marry within the fold, because it is better for the marriage, better for the children and better for Judaism.
However, in a free society there is no way of stopping some people from marrying non-Jewish partners, and no-one should feel frozen out of the community as a result. Every Jew, whether married in or out, is part of Judaism.
Positive involvement in Jewish life should be welcomed. This does not mean synagogues or rabbis officiating at interfaith marriages. Nor does it mean allocating synagogue or communal honours to people who have married out. But the community should rejoice that a Jew wants to remain Jewish, treat the non-Jewish spouse with respect, and welcome the family at Jewish events and celebrations.
Experience suggests that in time a number of non-Jewish spouses find Judaism sufficiently meaningful as to want to become Jewish themselves, and the children of non-Jewish mothers convert to and uphold the Jewish way of life.