I would question the validity of your comparison. There were absolutely famous actors and performers (look at the popularity of castrati like Caffarelli - sorry, I know music better than theater), just as there are extremely popular playwrights now (like David Mamet).

I don't have any credentials when it comes to this kind of history, so rather than trying to answer one way or the other, I'll ask: is it inaccurate to assume that actors are now more famous than playwrights were in their time, and is it even possible to make that comparison?

If you want a simple answer, it's because the actor is in front of the audience, but like /u/curse_of_kintave, I don't think your comparison is completely apt. It may seem to us today that playwrights from ancient Greece or Rome or Elizabethan England are more popular, but it is because their artifacts remain available for us to study. We have names of actors from those periods, but the work they produced survives only in anecdotal form (which is part of the difficulty in working on theatre history).

I'm not sure of the time period you're looking for with "back then," because theatre and acting has a history that dates back in records to 534 BCE. But, even the anecdotes that do survive tend to work against your question. Aristotle's Poetics makes such a big deal about Sophocles' Oedipus because he's writing about 100 years after the play was written and the theatre of Aristotle's time had become very dependent on star actors over the written word. We have names of some of those actors, but we can't say what their performance styles were like. (Actually we're still debating what performances of ancient Greek theatre were like to begin with - I think. This is a little outside my wheelhouse.) In Rome, Roscius was much, much more famous as an actor than the playwrights of the time.

While the answers here cover some of it, we also need to make a distinction between who would find these people 'famous' and/or be drawn to them.

Acting has a long history as being considered a lowly profession going back millennia. Indeed, Nero was pilloried by the Senate for deigning to perform as an actor and musician. This type of attitude carried on for most of European history into the early modern period. But this wasn't a universal attitude among the populace. Read the sentence about Nero again. Who hated that he did this, and scorned him for it? The Senate. The richest men in the Empire. For the wealthy nobility, acting and music were professions of scorn, but for the layman who might literally toil in excrement and piss all day, acting and music would certainly not be something to be looked down upon, and being a talented actor or musician would certainly give you fame and respect among the lower classes. On the other hand, playwrights almost always came from the learned and moneyed class already, even if they weren't necessarily nobility. Take Sophocles for example; he was born to a wealthy family and benefited from the luxuries (and most importantly, the education) that such provided. Or Shakespeare. Although not nobility, his family was reasonably well off and he was also afforded an excellent education.

So what was the source of the derision towards actors? I think we can begin to see that this is not strictly speaking a professional association as much as a class based one. Actors were generally part of the lower classes, while playwrights were part of the upper classes. Associating with an actor was as offensive as associating with any other lower class person.

That said, there are countless stories of nobility hosting actors and allowing them to participate in social gatherings, but this wouldn't be something one bragged about. More of an unspoken truth. And if it came out that Count Whatshisname was found cavorting with actors, well, what a shock! He is a brute! An uncouth ruffian of a man! Now, dear wife, can you invite that acting troupe to our next ball? They were ever so much fun...