Married Wirh Children was pretty unique for the 80s. I grew up during that time and not much else competes with it for edginess. The only show I can think of that got similar attention for being against the grain is The Simpsons but even that feels tame. Those were the two shows that seemed to get articles in newspapers about how upset mom and religious groups were. MwC was banned in my house.

You're just not going to find edgy network sitcoms from the 80s I don't think. There might be sketch shows like In Living Color that broke a lot of norms but network sitcoms were deep into family friendly stuff. Seinfeld kind of broke things out of that.

There's another show the creator of Married with Children did that has a very similar vibe called "Unhappily Ever After" but that came out in 1995.

You might have luck looking at paid cable comedies. But the only one that comes to mind is "Dream On" which aired in 1990