Q. Is it acceptable for male and female congregants to join in singing Adon Olam?
A. The Talmud (Sotah 48a) objects to two types of mixed singing:
1. When men sing and women then join in, and
2. When women sing and men then join in.
The second case is regarded more negatively than the first. The rationale of both appears to be that when one gender starts and waits for the second to join in, unholy thoughts may be aroused.
Rabbi J Simcha Cohen, formerly of Mizrachi in Melbourne and an acknowledged halachic writer, notes a third scenario which the Talmud does not record at all, i.e. when a community sings together in unison. In that situation the singing is not structured on male-female lines and neither men nor women are paying specific attention to the melodic tones of the other gender; they are singing as a community (“Intermarriage and Conversion: A Halachic Solution”, 1987, chap. 19).
However, this does not justify a mixed choir, which is, by definition, structured to take note of the different group of voices.