Bloomberg, who has led the city for 12 years, is well-known for his strict interpretation of the separation of church and state, The New York Times reported Sunday.
He has refused to add clergy to Sept. 11 commemorations and rejected a City Council resolution to add two Muslim holidays to the school calendar.
Voters of faith are now being courted by Bill de Blasio, a Democrat, and Joseph J. Lhota, a Republican, who describe themselves as guardians of freedom of religion. While saying they respect the desire of Bloomberg, who is Jewish, to maintain a legal distance between church and state, they claim he has ignored the needs of religious communities.
De Blasio and Lhota both come from Roman Catholic families. De Blasio says he does not attend church; Lhota says "religion is intertwined in my life."
Both men have pledged to add the Muslim holidays to the school calendar, although Lhota says he would extend the school year by two days to make up the difference. They also would allow churches to hold worship services in schools.
Additionally, they have said they would rethink Bloomberg's restrictions on metzitzah b'peh, an ultra-Orthodox circumcision practice in which blood is sucked from an infant's wounds.
Bloomberg requires parents of the infant to sign a consent form. Lhota says he would do away with the consent form, but offer information about the risks of the procedure. De Blasio says he would retain the forms until he could consult with religious leaders to find a better method.