How have Americans become so prudish toward sexuality yet so open to violence?

There is no simple answer to this, no one single factor in American history and culture which can account for such broad trends. The roots of them go back to the cultures of the original colonies, as maintained, modified, and overthrown by every subsequent generation and every wave of immigrants. But I can talk about a small, representative slice of Americana, and how censorship was applied there.

Pulp magazines emerged at the turn of the century from the dime novels and nickel weekly magazines. Their contents reflected the tastes of the day, and ran the gamut from the sedate to the risque, from the action-filled western and crime stories to the intellectual and philosophical. The early pulps catered to a broad audience of all ages and walks of life; anyone that could afford the dime or quarter was welcome to buy them at any newsstand.

There were limits on the content; mostly imposed by editors' individual tastes. While an early pulp might contain an artistic nude or a vicious villain, risque jokes for the college set, none of the publishers wished to run afoul of charges for obscenity (which, being broadly defined in the 1920s, could apply for gore as well as sex) that might get them arrested - or worse, lose them mailing and distribution privileges.

Such concerns were real: the New York Society for the Suppression of Vice was an active force in censorship in the 1920s, 30s, and 40s, all the way until 1950. They targeted works of literature such as James Joyce's Ulysses (1922), pornographic Tijuana bibles, works on birth control, collections of ribald jokes, pulp magazines, and anything else they felt within their remit. Pulp magazines like Weird Tales, which sometimes included nude women on the covers, faced internal conflict from readers for and against the practice; H. P. Lovecraft once famously opined:

I have no objection to the nude in art—in fact, the human figure is as worthy a type of subject matter as any other object of beauty in the visible world. But I don’t see what the hell Mrs. Brundage’s undressed ladies have to do with weird fiction!

— H. P. Lovecraft to Willis Conover, Selected Letters 5.304

Lovecraft was also less than thrilled with the violence in his friend Robert E. Howard's stories of Conan the Cimmerian, noting:

Robert E. Howard’s omnipresent gore-spattering is surely getting monotonous, but I fear it will prove a hard fault to eradicate.

—H. P. Lovecraft to Clark Ashton Smith, 11 Sep 1931, Dawnward Spire, Lonely Hill 322

Lovecraft of course made no effort to eradicate either the nudes or the violence from Weird Tales; to editor Farnsworth Wright, both practices had their sales value and their audience. The pulps could safely advertise for mail-order works on birth control or the mysteries of sex, often under the thin disguise of works on anthropology and ethnography; the Society for the Suppression of Vice's unwillingness to go after academic texts provided a cover for publishers to produce "dry" treatises like Voodoo-Eros: Ethnological Studies in the Sex-Life of the African Aborigines (1933), and works on flagellation and physical punishment which the Society did not recognize as "sexual" proliferated; Robert E. Howard himself owned a copy of Flagellation and the Flagellants: A History of the Rod in all Countries from the Earliest Period to the Present Time (1910) and several other works—not necessarily because of prurient interest, but as raw material for his stories.

The rhythm of the swaying bodies grew faster and into the space between the people and the monolith sprang a naked young woman, her eyes blazing, her long black hair flying loose. Spinning dizzily on her toes, she whirled across the open space and fell prostrate before the Stone, where she lay motionless. The next instant a fantastic figure followed her--a man from whose waist hung a goatskin, and whose features were entirely hidden by a sort of mask made from a huge wolf's head, so that he looked like a monstrous, nightmare being, horribly compounded of elements both human and bestial. In his hand he held a bunch of long fir switches bound together at the larger ends, and the moonlight glinted on a chain of heavy gold looped about his neck. A smaller chain depending from it suggested a pendant of some sort, but this was missing.

The people tossed their arms violently and seemed to redouble their shouts as this grotesque creature loped across the open space with many a fantastic leap and caper. Coming to the woman who lay before the monolith, he began to lash her with the switches he bore, and she leaped up and spun into the wild mazes of the most incredible dance I have ever seen. And her tormentor danced with her, keeping the wild rhythm, matching her every whirl and bound, while incessantly raining cruel blows on her naked body. And at every blow he shouted a single word, over and over, and all the people shouted it back. I could see the working of their lips, and now the faint far-off murmur of their voices merged and blended into one distant shout, repeated over and over with slobbering ecstasy. But what the one word was, I could not make out.

—Robert E. Howard, "The Black Stone", Weird Tales (Nov 1931)

Howard included such scenes in his stories, just as many other authors did, because including a nude woman increased the chances of getting a coveted cover illustration—which often brought a boost in pay as well as prestige. Making the nudity a scene of flagellation was a way to help get it past the censors, since the editor could point to the exact scene being illustrated, demonstrating it's "literary" value.

Other publications were not so discerning. As the pulp marketplace grew, it proliferated and diversified. Pulps were in constant competition to find new niches, and quickly specialized. Two in particular stand out in the late 1930s: the Spicy pulps, which focused on sex, and the Shudder pulps or weird terror pulps, which focused on grue.

Despite the name, the Spicy pulps sold the sizzle but not the steak; with their blatant focus on sex, they were obvious targets for censorship, and developed strict editorial guidelines about what to write and not write; illustrations and stories were routinely censored to be risque or sensual without crossing the line - often stipulating that a woman could not get entirely naked, or that a nude corpse was acceptable but not a living woman. Robert E. Howard wrote of writing for the spicies:

A nice balance must be maintained — the stuff must be hot enough to make the readers bat their eyes, but not too hot to get the censors on them. They have some definite taboos. No degeneracy, for instance. No sadism or masochism. Though extremely fond of almost-nude ladies, they prefer her to retain some garment ordinarily — like a coyly revealing chemise. However this taboo isn’t iron-clad, for I’ve violated it in nearly every story I’ve sold them. I’ve found a good formula is to strip the heroine gradually — she loses part of her clothes in one episode, some more in the next, and so on until the climax finds her in a state of tantalizing innocence. Certain words are taboo, also, though up to a certain point considerable frankness in discussing the female anatomy is allowed.

—Robert E. Howard to Novalyne Price, 14 Feb 1936, Collected Letters 3.19

Shudder pulps represented the other end of the spectrum: sadism was the rule. These were the pulps that often featured bound women on the cover, sometimes being tortured in inventive ways, buried or burned or swallowed alive, and the contents reached a peak of grue that the more mainstream pulps wouldn't touch. The sadism angle sometimes saved them from censorship, but New York mayor Fiorrello LaGuardia was still moved to ban the sale of pulps with nude covers in the city in the 1930s.

Pulps were the direct precursors to comic books, often sharing the same writers, artists, editors, publishers, and distributors. The group behind the Spicy pulps ran comic strips in their magazines, and eventually became DC comics. Martin Goodman published horror pulps like Uncanny Tales and Marvel Tales before switching to Marvel Comics.

The early comics, like the pulps, were varied and self-policing. By the end of World War II, as paper restrictions were relaxed, there were crime comics and romance comics, science fiction comics and westerns, horror comics and sex comics - although the more explicit of the latter were still sold under the counter, often produced crudely by small groups rather than major syndicates like DC. Most companies had their own internal codes and guidelines; Sheldon Mayer at DC provided one list of rules for writers and artists in the 1940s:

Never show anybody stabbed or shot.
Show no torture scenes.
Never show a hypodermic needle.
Don't chop the limbs off anybody.
Never show a coffin, especially with the body in it.

—Mike Benton, The Illustrated History of Horror Comics 52

Not every publisher kept to such strict guidelines, and crime and horror comics in particular would often be particularly gruesome, reflecting the standards of the shudder pulps that they ultimately emerged from. Here, though, something different happened: somebody thought of the children.