The discourse surrounding Rimitti is consistent with the usual world music accounts of rai music, which stress its "rebel" quality and tend to emphasize the antagonism between the rai rebels and Islam.
To his credit, Pareles' obit does (as do many other accounts) acknowledge that Rimitti made the hajj to Mecca in 1976 (some say 1975) and that as a consequence she gave up drinking and smoking. She did not, however, give up performing, and her songs continued to be "edgy" when it came to the subjects of women and sex. I do not have the space to elaborate here, but it should be asserted that there is no necessary inherent contradiction between being a believing Muslim and singing in public about women's issues, including sexuality. (Unless, of course, one believes that salafist Wahhabis get to define what "real" Islam is.) The key source to consult on these issues, when it comes to rai, is Marie Virolle's La chanson raï.
When I visited the Barbès district of Paris in summer 1992, I found this cassette in one of the many cassette shops selling vast quantities of rai tapes. It's the only recording I've ever seen where Rimitti is called "Hadja" rather than "Cheikha."
The tracks are: "Sidi Bouabdala" (I presume this is the name of a saint); "Ya Mohamed Ya Rassoul" (O Mohamed O Prophet); "Sinia Halouha"; Hamra Ou Baida (Red and White); "Haoulih Ya Zerga"; and "Ya Oulidi Ouankhaf Aalik."
As far as I can tell "Ya Mohamed Ya Rassoul" is the only track that is unambiguously "religious," but of course, to do such a set of songs and include a song in praise of the Prophet Mohamed was a way of making the other material (if it does indeed deal with "secular" concerns like male-female relations) socially acceptable. (Virolle has written about how [Cheb] Khaled has used the same mechanism as a strategy. He typically used the song "Salu' 'ala al-Nabi" (Praise the Prophet) to open or close concerts in Algeria during the eighties, as a means of making his other material, dealing with, say, alcohol and dancing, acceptable.)