Before someone comes in and tries to say "Blazing Saddles"
No.
Basically, the only sort of comedy that probably wouldn't get out of the writers room anymore is comedy that relies on a cultural acceptance of fairly oppressive/prejudiced notions as fact. And even then, that shit still slips through.
Otherwise, so long as you're challenging some sort of ingrained status quo with your satirical observances, pretty much everything is acceptable today. Whether or not you land your joke is a different question entirely. But unless you're shown to be a thoughtless, privileged, downward-punching dipshit, you're typically given some leeway to go where you're trying to go.
The notion that shit is somehow more off limits now than it was then is fascinating to see get regurgitated over and over again, especially by people whose knowledge of the past is entirely academic and not contextual or even drawn from personal experience.
Comedians get away with so much shit now. Comedies push envelopes way farther than they used to. Comedic storytelling fucking goes places it didn't used to on the regular when I was growing up, and the risks being taken in comedy are, from what I can see, bigger and bolder than they were back then, on average.