Twenty-first century popular media, including film, television, videos, and games as well as plays, present sexual acts, murder, torture and rape in full and realistic detail on stage or screen for the enjoyment of their audiences. In Greek drama, all of those acts would be presented offstage in tragedy; satyr plays (a form of comedy) would allow for stylized sexual acts (using six foot long leather phalloi), but not violence.
The main debating point on the modern side of the issue revolves around freedom of speech, and that, as argued by John Stuart Mill in his seminal work "On Liberty", we should allow all acts unless it can be proven that they cause harm to individuals within our society or our society as a whole. On a practical level, censorship simply does not work; despite, for example, the best efforts of international law enforcement to eradicate child pornography, it continues to exist. The next argument made in favor of explicit violence is that it occurs in reality, and thus should be shown as entertainment. The final argument in favor is basically a market one, that since some people eagerly pay to watch pornography, pain, and suffering, that free market economics mandate that buyers and sellers should be able to trade freely in such entertainment (this claim would also, of course, mandate legalization of child pornography as well).
The classical position, as applied to Oedipus Rex, is somewhat more nuanced. First Greek tragic staging does not aim towards realism but towards a certain dignity and grandeur. There were two episodes of violence that could have been presented directly on stage, Jocasta's suicide and Oedipus' stabbing out his eyes. There were several reasons for these and other forms of violence being performed off stage. First, there is the realism argument. Actors, whether in ancient or modern works, do not actually kill themselves or blind themselves on stage. Although all acting is unrealistic (an actor is always pretending to be someone else), the actions done by actors on stage in Oedipus consist mainly of talking, which is something they are actually doing. Actors pretending to be fighting or dying look artificial by contrast.
More importantly, when we see simulate acts of grotesque violence or perverse sexuality (e.g. if we had a bedroom scene with Oedipus and his mother), we tend to react viscerally and emotionally at a level that precludes actually thinking about or learning anything from the work. Although we experience some of that horror as we hear the messengers recount murders, or see Oedipus stumble out onto stage in a mask with blood painted around the eye area, we are invited to think about the events of the play rather than react simply on the level of emotion.
Finally, there is the issue that viewing violence brutalizes an audience by teaching them that human pain and suffering are forms of entertainment to enjoy rather than real ills in the world in need of remedy. By keeping violence offstage, it can still be part of the plot of a play without having that brutalizing effect upon the audience and without assenting to the notion that when we see people suffering as victims of violence that we should just sit back and pass the popcorn.