When we talk about Christ figures in literature, we are not necessarily talking about the historical Jesus or any sort of religious connection, but rather we are talking about an archetype, or common character pattern where newer characters exhibit similar traits to previously established characters. Rather than an exact template, archetypal characters exhibit enough traits from the pattern to establish a connection, but there may be some variations from other versions. So, if we set aside religion and spiritual belief for a minute, what are Christ's traits as demonstrated through his biblical narrative? He sacrifices himself for the good of others, he resists tyranny and oppression, he has disciples or followers, he performs miracles, etc.
So, while there are certain traits of Christ's which don't apply to Randal P. McMurphy (like being good with children or literally walking on water), there are many that do. For example, some of Christ's well-known parables are about fish and fishing (i.e. "I will make you fishers of men), and many of his followers are fishermen. McMurphy arranges an illicit fishing trip for the residents of the ward. Many of these residents have come to follow McMurphy and be inspired by him (his "disciples"). McMurphy performs some "miracles" (like making the paralytic Ellis walk), and he continuously resists the tyranny of Nurse Ratchet and the oppressive ward staff (as Jesus resisted the tyranny of the Romans).
McMurphy is a self-professed degenerate gambler and womanizer, and he readily admits petty crimes like the ones that got him locked up. At first glance, Christ does not resemble a criminal like McMurphy, but remember that many of Christ's actions (organizing followers and preaching to them) were considered blasphemous and illegal by the governing Romans at the time. Christ was an outlaw too.
The biggest sign of a Christ-figure archetype in literature is a character sacrificing oneself for the greater good. This one's not quite as clean in McMurphy's case since he is not necessarily "sacrificed," but he does give up a chance to escape in order to attack Nurse Ratchet, who he blames for Billy Babbit's suicide. McMurphy's resulting lobotomy and vegetative state inspires The Chief to escape. The Chief smothers McMurphy in an act of mercy and to carry his spirit along to freedom (a sort of resurrection?), and he lifts the tub room controls which McMurphy could not previously budge (a miracle?) in order to make his escape. So, it could be argued that McMurphy sacrificed himself for the good of The Chief.
While certainly not a one-to-one correlation, a strong argument can be made for McMurphy demonstrating a number of traits which would make him a Christ-figure archetype.