I'm not referring to the urban legends about her sex life, obviously those aren't true. Still, Catherine the Great had many lovers over the course of her life that would be unconventional and even considered unambiguously sinful by the Russian Orthodox Church, being enough to damn a person's soul.
She also defied gender stereotypes in general, even having a tattoo. From what I've read about her, she was a devout Orthodox Christian, demanding an Orthodox priest when she almost died of sickness, converting to it against her parent's wishes, and overall holding a deep respect for it over her life.
How did she reconcile her faith with her lifestyle choices? Bonus question, how did the Russian Orthodox Church view it?
The short, unsatisfying answer: Catherine likely wasn't very religious.
The Romanovs long had a strange duality between Orthodoxy and personal affairs. Essentially, just about all Romanov monarchs, except the first three, Mikhail, Alexei, and Fyodor - and the last two, Alexander III and Nicholas II, took lovers.
Essentially, the church had lost power against the Romanovs. During the reigns of the frail Mikhail and then the deeply religious Alexei, the Orthodox patriarch was effectively the co-ruler.
This system didn't ultimately last, as the two found it too hard to share power.
Then, after the brief reign of the ill and (possibly mentally feeble) reign of the sickly Fyodor, the church was to further lose influence at the top corridors of power.
Peter I, later known as Peter the Great, unleashed secular, European-style modernising decrees.
Peter, who, was by modern standards an agnostic, was disliked by the church (to the extent that some saw Peter as the antichrist), but the church, which was loyal to the state, couldn't do much against him.
By the time Catherine showed up, Romanov monarchs simply had huge power in the modern state Peter built. Russian palaces have chapels built in, and Catherine spent time in religious ceremonies.
But, in a paraphrase of her own words, her heart ached for love - the love of a variety of different men.
Whether or not Catherine truly cared about Orthodoxy - or in her cunning merely found embracing the faith pre-power to be convenient, is up for debate.
EDIT: In Catherine's own aborted memoirs, she rarely mentions faith - or her affairs. The memoirs seem mostly devoted to the intrigues of tsarina Elizabeth's somewhat chaotic court at the time.
Perhaps the real Catherine is better found in her love letters to her lovers.
Catherine's letters drip with radiant passion, but as she a lady raised as a prudish Prussian protestant princess, pay scarce mention or detail to sexuality.
You can find out more about Catherine's love life in Robert K Massie's Catherine the Great.