From what I understand one of the big ways in which Nero shocked proper Roman society was by personally performing on stage, which I'm told was treated with about as much respect as prostitution.
But everyone likes music and to be entertained, and in the days before TV and recordings I would have thought entertainers would be MORE treasured than today. Why did Romans looks down their noses at musicians and actors?
First, disclaimer: Ancient Rome is not my area for this (China is) but I have dug into this a little in my reading.
Both prostitutes and actors were classified legally as infamesin Augustus’ moral legislation. This was in part because they were viewed as faking emotions for money, and both groups also engaged in cross-dressing. The root of your question comes down to the phenomena described by Bakhtin as “the low-Other” in society which was further refined by Stallybrass and White as a commodification of desire for the low-Other by those at the top of the social hierarchy in their bid to maintain social control.
That is, prostitutes and actors were on the same social level, and playwrights took inspiration from the work of prostitutes as that of equivalent to actors and repackaged them for consumption by the masses as both entertainment and cautionary tales. The stock character in Roman Comedy of the meretrix is almost always either a “hooker with a heart of gold” type or “heartless man-eater only out for the money” type, and are either commended in the text of plays as support for the main male or denigrated as villainous. There were even direct comparisons between acting and prostitution as professions that fake emotion in the plays.
In Roman cities neither actors nor prostitutes were segregated from the rest of society—unlike in Renaissance England, or China and Japan. Actors could be legally subjected to being beatings in the streets by Roman citizens, though this was later restricted to only while they were on stage. That actors would satirize powerful political or social figures did make them entertaining to the general populace, but it also was extremely risky. Gladiators were also classified as infames, and their audience was highly entertained, but this doesn’t mean they were of high social standing like members of professional sports today. So, too, with actors and prostitutes.
And that’s what Stallybrass and White point out: the top of the social food chain will co-opt the figures of the lowest classes for entertainment value initially and then will strip those figures and art forms from that low-Other and realign them with the upper class paradigm. That the 19th century and early 20th century changed the view of acting from a low-class activity and divested it of much of its relationship to sex work and transformed it into an elite class of celebrity has more to do with the growth of capitalism and industrialization than it does the craft itself.
Sources: Faraone, Cristopher, Christopher A. Faraone, and Laura McClure. Prostitutes and Courtesans in the Ancient World. University of Wisconsin Press, 2006. Stallybrass, Peter, and Allon White. The Politics and Poetics of Transgression. Ithaca, NY: Cornell Univ. Press, 1995.