One particular choir director/concert pianist I've worked with commonly used the term "soprani" (although she did not say "alti," "bassi," or "tenori").   It would not have seemed strange, since so much musical terminology is in Italian, except that the way she pronounced "soprani" it rhymed with "granny."   Because of that, for some time I thought she was clowning around when she'd say "soprani."   Had she pronounced it to rhyme with "Giovanni," I don't think it would have sounded any more odd than "andante" or "pianissimo."

But in my experience, "castrati" is quite common. (I mean to say the WORD is, not that THEY are.)