A fluffy bunny is a person who uses deliberate ignorance about his own professed religion to make that religion into whatever he wants it to be. While the term originated in Wicca, it has also been applied to those claiming to be Christians.
Fluffy bunnies tend to make sweeping statements, with no evidential basis, on their religion and even on God's will. They also tend to exalt the form of their religion (often exaggerated) over its substance and make a spectacle of their religious observance instead of showing how their supposed faith has borne fruit in their lives.
Christian fluffy bunnies take great offense when shown Bible passages that contradict their (mis)understanding of Christianity and seldom consider those Bible verses enough to repent and accept genuine Christianity. When they have the power to engage in liberal censorship against such Bible passages, they do so. They also often attempt to turn Christianity into a purely or predominantly secular political movement, emphasizing social justice and other notions that are completely unmoored from Bible-based Christianity. In doing so, they render their Christian witness ineffective or even damaging.
Bible-believing Christians often use the term Shirley god to rebuke fluffy bunnies who speculate about God's will by saying, "Surely God ...." Since "Shirley" and "surely" are homophones, the implication is that fluffy bunnies worship a false god, here nicknamed "Shirley," rather than the God revealed in Scripture.