Fourteen girls died in the blaze and dozens were injured.
The rare public discussion about the mutawaeen comes amid much anticipation of reform in the kingdom, ruled largely by royal decree with an unelected parliament.
Businessmen and well-known Saudis in January petitioned the royal court asking for elections, more rights for women and equality among the country's diverse social groups.
There has been growing domestic and foreign criticism that giving religious leaders a free hand to act, preach and police society fosters the kind of fanaticism and intolerance which encourages young Saudi men to become suicide attackers.
Religious figures are concerned that pressure is mounting to crowd them out of public life.
A statement issued by prominent clerics has said "extremist writers" are using the Riyadh blasts to attack the religious establishment.
And in a recent interview Grand Mufti Sheikh Abdul-Aziz bin Abdullah al-Sheikh, the kingdom's top religious authority, rejected calls to dismantle the morality police.
Anthropologist Saad Sowayan said the Saudi royal family would never scrap the morality squad because it bolsters their own rule, which has involved decades of absolute power.
But he added that the authorities could use the mutawaeen to advance reforms, as King Faisal did in the 1970s to push education for women and the spread of television.
"The government should choose people among the mutawaeen to justify reforms today. People will accept anything more readily if it is framed in a religious discourse," he explained.
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