It seems like adults have always liked animation better than puppets. There's been many primetime and adult puppet shows that have been hits (but there's also been a lot of failed primetime/adult animated shows and films).
Of course we all know that Jim Henson had trouble getting networks interested in The Muppet Show. Recently on a Muppet Facebook group I wondered outloud if the Muppet segments of Saturday Night Live would have been better received if it had established characters and somebody said the hatred of the segments on SNL came more from a stigma of puppets being "for kids" and the writers/cast/audience likely would have disliked them either way.
Greg the Bunny came at a time when it seems many were trying to put out more adult puppet shows, just a few years after the networks suddenly put out a lot of more adult animated shows. And it seems adult puppet shows fail more often than they succeed. This came out around the time of Avenue Q. which was a success (would Craig Shemin have been correct that it wouldn't have lasted if it was a television series like originally planned?), and just before the more successful Crank Yankers and Wonder Showzen. At the time Greg the Bunny came to Fox, it was announced that FOX was developing a new edgier Muppet series (which didn't get made after all). And of course The Muppets in 2015 was promoted as more adult (though usually tamer than most adult animation) and did not last.
I watched Greg the Bunny each week it was on. It seems it was a lot tamer and more appropriate than the promos made it out to be. I think I saw on Wikipedia a long time ago that one problem was that the FOX censors made them take out a lot of stuff but then the promos heavily focused on the most inappropriate stuff that was allowed to make it to broadcast.
At one point, without warning, they temporarily took the show off the air and put The Bernie Mac Show in its timeslot. I thought the show was just okay but after this I started to really hate The Bernie Mac Show (and I also grew to hate Bernie Mac, of course it took me a long time to realize it most likely was not his decision).
Not too many people I know openly watched it. A few people from my scout troop watched it, and one of my cousins and his friends watched it (I was pleased one day to see them quoting lines from the show, when I previously had not discussed the show with them). But I'd talk about it to people at school and they'd usually say they didn't watch it or didn't seem to care about it (seems to be the case with a few other shows I was a fan of at the time, like Titus and Baby Bob).