Since the Church was involved in music of the period, and since the Church kept monks separate from nuns, should the alto and soprano voices of a male ensemble be sung by a boy and a castrato?
As a classically-trained, professional musician, I feel I can comment on this a little. Depending on the ensemble's resources and skill level, they usually strive for as much historical accuracy as possible. For example, on a Bach piece, a professional symphony using gut strings versus a community orchestra using steel strings because they can't afford gut strings. Or, in the case of a choir, they might not have the proper membership for an all male ensemble. It's often a musician's or director’s responsibility to accurately portray a piece of music, as if they're a sort of historical reenactor. So, it might be a little anachronistic but it's usually not completely inaccurate.
Yes, soprano and alto voices should be sung by men or boys. They were usually sung by boys or men with a good falsetto back in ye olden times. But, it depends on the composer's original intent. IIRC, castrati weren't common enough to make whole choirs out of them. And you'd probably be arrested if you were making castrati nowadays. Women don't sound all that different from men singing the same note. A layman usually can't tell the difference. That’s where I think the responsibility lies on the listener. They might want a recording that sounds “close enough" to the original. Or they might want a historically accurate recording. The listener needs to find a recording that suits their needs.
Edit 1: a word.
Edit 2: It was only in sacred music that the church was involved. Other secular music, like Madrigals or Troubadour music, used men and women all the time.
It really depends on the type of music being sung. There's a great deal of history of men and women musicians (the Troubadors and Trobairitz) who performed secular music together frequently.
If you're talking about Gregorian chant, or Plaintchant, yes, it would typically be performed by a group of monks, or a group of nuns, but rarely, if ever, both.
As far as Castrati, they weren't really even in existence in any degree until the 16th century.
Can you be specific as to what kind of music you're referring to?