As part of this effort, the tsarina forced the Russian Orthodox Church to stop seeking new converts in Muslim lands and accept a kind of religious pluralism.
Critics maintain that pressures on Muslims to convert to Orthodox Christianity did not disappear, regardless of St. Petersburg's stated policies.
Catherine professed a belief that every Russian subject had to have a religion, but it did not necessarily have to be Russian Orthodox Christianity.
Historian Crews explains that Catherine was essentially pragmatic.
"Catherine II had seen from her predecessors that attempts at repressing non-Orthodox Christian faiths had led to violence and had in many cases failed," Crews says, "and had made the task of constructing an empire more difficult and more costly."
That didn't mean that the Russian state would leave religious matters alone -- quite the opposite.
Co-opting Muslim Leaders
Crews argues that Catherine was heavily influenced by 18th-century French thinkers who thought religion provided "an alternative means of social discipline."
"The regime sought religious support for its policies," Crews says. "In other words, it tried to co-opt local Muslim authorities who might be in a position to confer some kind of religious legitimacy upon state policies in order to reduce the chance of resistance."
Having studied the Ottoman Empire, Catherine and her advisers wanted to create a hierarchical Muslim structure that would work in tandem with the Russian state.
This was easier said than done, since many Muslim clerics advocated having nothing to do with the Russian state.
But Catherine eventually found a few figures open to collaboration.
They received not only a nice wage from the Russian state, but they also were able to use the authority of the Russian state and its police organs to advance their own status within their community.
Crews says Muslim clerics also learned to use to the Russian state to intervene in their own intense religious disputes, and to harness the state's resources for their own proselytizing efforts.
"In the 18th century along the Russian frontier which is now Kazakhstan, the Russian state found local mullahs who, in exchange for a salary, agreed to accompany Russian expeditions to go to the Kazakhs to 'missionize' among them," he says. "Here you have a clear example of mullahs who -- though working for the state -- were clearly advancing what they saw as a conversionary process among the neighboring Kazakh people, whose religion these mullahs thought was misplaced or simply -- in a word -- incorrect."
By sifting through the archives in Ufa, the capital of the central Russian Republic of Bashkortostan, Crews found out not only what the mullahs were up to but the villagers as well.
Crews says simple peasants petitioned the tsar or his ministers on a whole range of disputes.
For example, a woman who was being abused by her husband could -- and did -- appeal to St. Petersburg for a divorce. She could file a petition to the tsarina at the local police. Then it would go to the governor and then to the Russian capital. Tsarist officials would reach some resolution either though the offices of the highest Muslim authority or through the Interior Ministry.
And then, the order would pass back through the chain of command transmitted to the village or to the local policeman who would enforce it.
In this way, the Russian state reinforced its legitimacy by functioning as an arbiter not only in disputes among the Muslim elite but also at the local level.
"You have a very dramatic expose in these [archival] documents of how the empire functioned. You have a local village very far away from Moscow in which men waged disputes with their wives, with their children, with other villagers, all in a way that draws in the Kremlin as a kind of referee in these very intimate disputes -- that are very distant from perhaps the way we think modern governments function, but were very much a key to how these disputes were resolved in these distant locales, and most importantly were so important to how the empire held together and why it lasted for so long."
Crews warns that the Russian empire's techniques should not be applied today, despite its gains, since it would make governments "arbiters of religious affairs."
He says there is a desire on the part of British authorities to better integrate the country's Muslim populations and "create a single authoritative Muslim voice to sign off on British domestic and foreign policy."
"It would create a kind of uniform Islamic doctrine that would encourage integration, and it would combat what they see as a terrorist threat coming from British-born Muslims," Crews says. "But the risk in this means that the state becomes necessarily an arbiter of religious affairs, which is a major step back from a long and messy history of 20th-century political dissent, which the main goal has been to ensure certain basic civil rights. The policies the Russians have instituted and have made a mainstay of Russian political life is now paradoxically become a negative model for European states."
While Catherine the Great's approach to Islam may not be explicitly influencing Europe, her legacy is apparent in Central Asia today.
Catherine created various regional ecclesiastical assemblies for Muslim clerics that were later reworked as Muslim spiritual boards or spiritual administrations during the Soviet regime.
When the Soviet Union fell apart, the national republics retained these institutions. But now they answer not to Moscow -- but to Tashkent, Dushanbe, and the like.
Central Asia's leaders do not need to maintain control over a far-flung empire, as Catherine did. But like Russian imperial authorities, they have sought to reduce the influence of Muslim clerics from abroad -- for instance, from places like Saudi Arabia or Pakistan.
They want to bolster the authority of homegrown, state-sponsored religious authorities.
The goal in more than a century ago was finding Muslims leaders with legitimacy in the eyes of their followers and sufficient loyalty to the state. Some would argue that today's leaders face a similar challenge.