There's an interesting piece at Le Monde on Islamist efforts to ban or suppress the 1,001 Nights, a perennial target. It's fairly detailed and, while it also talks about campaigns against belly-dancing (a subject also overdue for an updated report here), it mostly concentrates on the Nights and its role in Arabic popular culture and entertainment: Les Frères musulmans font taire Schéhérazade (The Muslim Brothers would Silence Scheherezade.) This is not the first time of course; there was an effort in 2010, and various editions of the work have frequently come under fire. (As an aside, this appears to be a post on what is seemingly "Le Monde's sex blog". Who knew? I mean they're French and all, but so stuffy and intellectual ...)
The Western media tends to focus on the culture wars aspect of Islamist puritanism, since most of it is fairly straightforward: attempts to ban alcohol, or belly-dancing, or certain movies, or bikinis on beaches catch the Western imagination. Literary censorship is less frequently reported because it's harder to illustrate (though Le Monde does a pretty good job). And while many people may be at least aware of the erotic content in some of the Nights tales, most people probably associate them with Sinbad's adventures, or Ali Baba, or Disney's version of Aladdin.
Islamists (by no means just the Brotherhood, despite the article's title) are, like censors everywhere, more than willing to put their own persons at risk by finding all the dirty words or suggestive scenes in even enormous collections like the Alf Layla wa Layla, in order to protect us weaker creatures from them. This huge collection of tales may have roots in India and pre-Islamic Persia, sets many of its tales in the Abbasid Baghdad of Harun al-Rashid (but others as far afield as China, the distant seas, or the kingdoms of the jinn). Collected over centuries and varying according to the taste of the storyteller, they are tales of ordinary human beings (and a few supernatural ones of course), with all the flaws and failings of ordinary human beings. There is no shortage of infidelities (one even underpins the framing story: King Shahryar is killing a new bride each night because his queen was unfaithful), and sexuality, both straight and gay, is taken as a part of life. That probably reflects the reality in Arab and Persian cities in the classical age, where these stories took shape. It is reflected in the poetry and more serious literature of the day as well, the day when Islam led the world in science and astronomy and mathematics and medicine, but it is not the portrait of a golden age of Islam the Salafis want to encourage in their followers.
As a whole, to approach the 1,001 Nights as essentially erotic in its content is misleading; it is far too varied for that, and there is nothing objectionable in many of the tales. On the one hand Islamists are trying to ban the whole for a few of its parts, like American school boards who ban books from high schools due to one or two objectionable words. But I think a point made in the Le Monde article is important: the tales are also full of strong, independent-minded women, easily equal to men, and none more so than the narrator herself, Shahrazad or Scheherezade, who not only seemingly knows every story ever told, but whose ruse lasts for 1,001 nights and saves her life. King Shahryar, by contrast, comes across as a rather dim bulb. Of course her stories captivated him so he let her live each night. (Since the framing story says she also bore him three sons during the period, they must have taken some breaks from the tale telling, yet he still didn't catch on.)
According to the article there have also been efforts to replace Shahrazad with a male narrator. Perhaps the real objection is not just the (occasional) erotic passage but that narrator who constantly runs rings around her rather slow-to-catch-on husband.
The 10th century Arab bibliographer Ibn Nadim in his Fihrist describes a Persian work called the Hazar Afsana (1000 tales) that originated in pre-Islamic Sassanid times; Masudi in the same century mentions that there is an Arabic version called the Alf Layla (1000 nights). They picked up an additional night (and a lot of additional tales) over the centuries, but the stories have been around for over 1,001 years by now. I think that, rage and burn books though the Islamists may do, the clever tellers of the tales will, like Shahrazad, outsmart the dense ruler and guarantee the tales live on.