Whilst curious to read about Harry Kemelman, the originator – as I understand it – of the Rabbi sleuth, I came upon Clerical Detectives.
Philip Grosset categorises some 250 characters in various ways, most interestingly by religion . The categories include:
Witches and he adds in brackets (who mean well)
Nuns (separate category for medieval)
Needless to say, Protestantism and Catholicism dominate.
For Jewish, rather than literary discussions of Kemelman see