Question: Does Judaism allow for an uncle and niece to get married?
Answer: You ask about the Jewish custom of marriage between a man and his niece. You have more than a passing interest in this topic, as your grandfather and grandmother had this relationship. Further, you state that your mother, yourself and your two siblings all suffered debilitating diseases, including multiple sclerosis, Crohn's disease, and mental illness.
I can understand that you have strong feelings concerning marriages between uncles and nieces and that it causes you considerable pain to consider that the suffering of your family might have been avoided if your grandparents had had a different attitude toward this kind of marriage. One can only sympathize with your suffering.
I'm not a doctor or geneticist, so I can't really comment on whether there is a connection between the illnesses in your family and the consanguinity between your maternal grandparents. I have read that the incidence of genetic disease among the children of first cousins is between four and six percent, about double that in the general population. I would imagine that the rate is higher among the children of uncles and nieces, who are more closely related than cousins.
Traditionally, Judaism does permit marriages between uncles and nieces. In fact, it is considered in the Talmud to be a meritorious match (B. Yevamot 62b). By the late medieval period, however, at least some Jewish legal authorities wished to end or limit the practice. For example, Sefer Hasidim declares that a marriage between an uncle and niece "will not be successful," an apparent effort to discourage the practice.
Permitting and encouraging marriages between close relatives is not at all unique to Judaism. Many cultures regard different forms of endogamy (in-marriage) as permissible and desirable. (In witness to this, consider the frequent marriage of close relatives in royal families.) American law is less accepting of marriages between first cousins, for example, than the laws of Asia and Western Europe, for reasons that seem to have more to do with American culture than with science.
Marriages between uncles and nieces generally are not permitted in the U.S., and, as such, are not officiated by Reform rabbis.
With best wishes,
Rabbi Jeffrey Goldwasser