Cat's Cradle has no doubt very strong postmodernism philosophies embedded in it. If one were to inspect the religion Bokononism closely, there are many connections with the religion and postmodernism.
Postmodernism deals with a movement founded in the 18th century that wanted to reject the ways of modernism. Postmodernism has no distinct center on it and has no one controlling source which it originates from. An easier way to differentiate postmodernism with modernism would be an example of a painting. Consider postmodernism as an abstract painting with random, spontaneous lines and colors. The Modernist painting however, would be the painting that would feature an actual drawing such as a portrait or landscape.
The founder of Bokononism was Lionel Boyd Johnson, whose name was corrupted by the island dialect. Bokononism contains the postmodernist misreading, combination and anarchy at once. Even the first verse in the Book of Bokonons says: "All of the true things that I am to tell you are shameless lies." Here, voneggut's opinion on religion actually comes out; that people always look for something to what they can believe. "Truth was the enemy of the people, because the truth was so terrible, so Bokonon made it his business to provide the people with better and better lies." Here you can see how bokononism relates to a play of sorts. All the so called "followers" are like actors that are fed with lies and like any other major religion, follow it blindly. Thus, I think Vonnegut is trying to satire the concept of religion in the novel by exposing how fradulent the religion actually is. This a postmodernist feature, which is typical for many postmodernist books. The main faith is not based in some religion, but in man himself. In Postmodernism, this is the exact idea they were getting at. By eliminating lies and the myths that society holds, they become all that more powerful. The people who came up with Postmodernism came to believe that science is the power of logic, which seems to tie in with the scientist's idea in Cat's Cradle as well.