When did it become acceptable for movies to have nudity, graphic violence, and profanity?
This is a really deceptively complicated question. First we have to consider: What part of the world are we talking about? Do you only care about America, the West, or the whole world? Do you want to know where it was first regarded as okay for movies to have nudity and graphic violence, or do you want to know where it was broadly acceptable?
The second thing we have to ask ourselves is, what do we mean by nudity, graphic violence, or profanity? Is this provocative shot of Dorothy Mackcaill in Safe in Hell (1931) "nudity?" Is the notorious shot of an eye being slashed open with a straight razor in Un Chien Andalou (1929) "graphic violence?"
The third thing we have to ask ourselves is, what do we mean by "acceptable?" If someone shows a film containing nudity or violence and doesn't get arrested for it, is that "acceptable?" And conversely, do we take the backlash against "immoral" films prior to the Hayes Code as indicating that those films were not acceptable?
There's an evidential problem, too, with answering this question: The vast majority of early cinema is lost to us. We can't really know for sure when someone first had the bright idea of training a movie camera on gore or boobs, let alone when the first exhibition of such a film happened, and whether it was "acceptable" (Whatever that means). It's entirely possible that some wealthy Frenchman in the 1890s had a "private party" involving such a film at one point, it was a smashing success, and we have no way of knowing about it.
When it comes to mainstream American film, the most notable point in time I can give you is the introduction of the modern MPAA rating system in 1968, which made mainstream distributors once more able to distribute movies containing violence or nudity under the R, X, and later NC-17 ratings. Soon after the system's introduction, films such as A Clockwork Orange and The Last Tango in Paris became hits.
hi! Assuming you're referring to American movies, I'll throw you a few posts that discuss the Motion Picture Production Code, aka Hays Code, which was a film censorship program in the USA in effect between 1930 and 1968. These will give you a start on the general scope of censorship that had been in effect during that era: