Generally, we follow the traditional definition. That means that we consider a person Jewish if their mother is or was Jewish or if they have converted. We are probably more informal than most other Conservative congregations.
If a person fits those criteria, but has converted to or is practicing a conflicting religion, even though they may be technically Jewish, their status is similar to a non-Jew, and they may not be members of Beth Sholom. Primarily this boils down to those who believe the Messiah has already come once in the form of Jesus/Yeshua. We live a country where people can believe whatever they want, however as far as I know, no branch of Judaism accepts these beliefs. Please respect our beliefs.
The definition in the first paragraph also means that a non-Jewish spouse is technically not a member. Except for voting in congregational general meetings, certain religious functions and some leadership positions. In practice, non-Jewish spouses who were/are interested have been very involved in the congregation.