The Catholic Church, which has had a very dominant position in Italy for many hundreds of years, and the Mafia in Sicily is indeed a weird combination. I beleive, especially among the early Mafia members, the worship of Catholicism was genuine. Every religious person interprets the religious message differently and uniquely. To some extent, maybe, the Mafia members praid to god before carrying out a successful murder assaignment. I don´t know, but perhaps the weird combination of being a religious follower of Cathollicism and a Mafia member at the same time can be explained by the sacrament of confession which is highly revered by Catholics. And of course often taken advantage of.

Joe Profaci, for example, was an extremely religious person. One of his brothers was a priest, a sister was a nun and he had very strong ties to the Catholic Church in Brooklyn. Salvatore Maranzano had studied to become a priest at the same time he was "studying" to become a mafioso. It doesn´t look like they were ever bothered by the fact that they actually were committing sins. Perhaps they didn´t look at their transgressions as sins?

According to several accounts, there have been priests in the Mafia...full fledged members. I doubt they went around killing and stealing but they certainly enjoyed and took advantage of Mafia membership. And vice versa of course, the bosses prospered with having priests in their ranks.