The differences in how sexuality and violence are separately percieved are complicated and multifaceted as all hell. Thing is, the Anglo-American view on those two topics may have its roots as far back as the 16th / 17th century. See
this answer on AskHistorians, which talks about the "invention of privacy" as well as how police were initially unable to enforce public decorum. The more conservative notions on sexuality slowly but surely set in from there. Doesn't mean people didn't talk about it, of course, but it was much less in the public arena.
It's also important to remember that - and least in the UK and the US - the concept of "public" and "private" spheres survived in some form well past the 19th century, when those concepts were lifted up as ideals. The "public" and "private" spheres drove a lot of ideas regarding how men and women respectively were "supposed to" behave, Of course, societal changes leading up to the 1960s and beyond began to change public perception of sexuality - but sexuality is still very much a private matter for the most part.
Violence was also heavily targeted by moral guardians and public discourse, but not as much as sexuality. That's not to say it wasn't targeted - Victorian moralists were heavily concerned with violence and disorderly conduct (a reason why the Jack the Ripper murders became so infamous fast), especially in connection to alcoholism. Concerns over violence in American media was likewise a present factor throughout the 19th and 20th centuries - Hays Code also targeted violence to some extent, as well as later censoring of Looney Tunes cartoons as examples. But one possible key difference is that violence was never fully treated as a private matter - violence was arguably always in the public eye, whether in real cases or in movies. The classic "
Wilhelm Scream" comes after all from a guy getting bitten by an alligator in a war movie. That same scream was reused in quite a few Western movies, and became a staple with Star Wars.
Still, you only need to go back 30-40 years to find a very powerful Moral Guardian lobby - Moral Majority and related groups - concerned as all hell over both violence and sexuality (cartoons like the Get Along Gang were heavily affected by them), and as late as the 2000s you had people like Jack Thompson publicly targetting violence in video games (especially GTA and Mortal Kombat, but Thompson also targeted Doom). Similar groups still exist, mind, but they're no longer a driving force primarily because the Internet is so widespread and it's incredibly easy to find media - incl. video games - with violent / sexual content. Violent content does remain somewhat more visible, and violent content aren't treated as a private matter as much as sexual content is.
Again, this is primarily from the Anglo-American context. The European context is similar, but differ in a few areas.