Is there a halakhic basis for excommunicating a family member who intermarries?
ב"ה Shalom I don't know if this is a theoretical question or a practical one., so I will deal with both sides. In theory, Rav Yechiel Weinberg zt"l in his sefer Sridei Esh, Vol.I ,7 wrote that the act of someone marrying a non-Jew is an act which warrants excommunication and even though in practice the excommunication is not carried out in our times we would relate to that person as if it is carried out and such a person would be able to become part of a minyan. Historically, in the past when a child had intermarried, the family would sit shiva, as if the child had died. However, with intermarriage so rampant, unfortunately, in our times this way would not be a deterrent. Therefore, if this is a practical question of what to do if someone in your community has married a non-Jew, this is something which must be dealt with by the local Rabbi. There are considerations of creating deterrents for such action so as not to give it any legitimization on the one hand, but on the other hand not severing ties with people so that they do not become totally lost to the Jewish community. There are considerations not of not to flatter someone because of one's status in the community on the one hand, but also considerations of how not to lose somebody to the Jewish community. (For further reference see: אגרות משה חלק ב:נא, יחווה דעת חלק ב: טז, מראה הבזק חלק א: ז-ח,י, חלק ב: ט, חלק ד: יט, כה, חלק ה: יח,יט, All the best שנה טובה וגמר חתימה טובה