Papal infallibility is one of the main Protestant objections to Catholicism—yet, oddly enough, it was one of the things that gave Catholicism an unlikely avant-garde cachet from around the time of Pius IX's proclamation to, say, World War II. Particularly in England and France, artists and writers who had a particular bent towards modernism often were attracted to the Roman church. In England, home of Henry VIII's schism and a long history of antagonism with Catholic France, conversion was, for a time, the upper-class anti-Establishment gesture of choice, inspired by the famous apostasies of Cardinals Manning and Newman. Oscar Wilde flirted with Catholicism as an Oxford student in the 1870s, based in large part on the elegance of Newman's prose (one of the only things that kept him from taking the plunge was his father's threat of disinheritance). Wilde evetually decided his subversive tendencies led in other directions, but he's a prime example of the rebellious attraction of Catholicism for up-to-date Victorian college students, the 19th-century equivalent of a Che Guevara poster. (Note that, in England, this was mostly an aristocratic impulse—Edward Elgar, for example, felt his own outsider status had more to do with his working-class roots than his Catholic upbringing.)
The paradoxical modernity of Catholicism was even more explicitly perceived in France. The clearest statement of it is probably Guillaume Apollinaire's long poem "Zone," published in the collection Alcools in 1913. He name-checks Pope Pius X (who, coincidentally, had reduced the number of Holy Days of Obligation from 36 to a more manageable eight in 1911):
Religion alone has remained entirely fresh religionApollinaire adopts the conceit that technology is only aiming for what the church has already achieved:
Has remained simple like the hangars at the airfield
You alone in all Europe are not antique O Christian faith
The most modern European is you Pope Pius X
It is God who died on Friday and rose again on Sunday(Translation by Roger Shattuck.) One can start to see the attraction of Catholicism, bestowing a miraculous poetry on technological advance, while anchoring the dizzying speed and confusion of the modern world in archaic ceremony. Some saw its strictness as a bulwark: Wilde (who eventually converted on his deathbed) once made the unlikely claim that Catholicism might have tempered his homosexuality, while Jean Cocteau, the most self-conscious modernist of all, briefly returned to the church in the late 1920s while unsuccessfully attempting to overcome an opium addiction.
It is Christ who soars in the sky better than any aviator
He breaks the world's altitude record
But mostly, I think that modernist artists and writers, attempting to create entirely new worlds by fiat, saw a kindred spirit in the all-powerful, deliberately ancient pontiff. The high modernism of the pre-World War II era was as much backward-looking as forward: Stravinsky's neo-Classicism, Pound's neo-Medievalism, the influence of Greek antiquity on Picasso. In a culture saturated with jazzy modernity, the sort of bracing anachronism exemplified by the Catholic church could seem the most avant-garde movement of all.
This sort of relationship has never been far from the surface in music, which turns again and again to the past for structure, inspiration, or effect. There's a fair amount of Renaissance influence in post-minimalist music, but, then again, there was also a fair amount of Renaissance influence in serialist music, too—Webern's expertise in the music of Heinrich Isaac bore fruit in just about all of his own compositions. Punk rock was in many ways a return to the 50s; today, almost the entire pop spectrum can be read in terms of retro influences, be it AM-radio easy listening, 70s soul, 60s psychedlia, Basement-Tapes-style recycled roots music, etc. All over the map, yet, I think, traceable to the same post-Romantic impulse that made the cutting edge a fellow traveler with Catholicism for a while: not just the shock of the new, not just the reinvention of ancient innovation, but a necessarily foolhardy assertion of the infallibility of the artist's taste. The appeal of Catholicism was not just its discipline, but also the model of its hierarchical theology. The dogmas vary, even from work to work, but the ability to decide what they are remains the creator's fundamental privilege. Every piece is an encyclical: we claim our own imprimatur.