My dad let me watch Futurama from a pretty young age, basically since I was 7-8 years old. (Much to my mom’s annoyance) Even though it had adult jokes in it, I watched and loved it like any other cartoon. This led to me getting in trouble in after school because I drew Bender saying “Bite my shiny metal ass.”
Also, my dad let me watch The Daily Show and The Colbert Report with him every night, even though I didn’t know a thing about politics for years. I just liked the fact that there were two shows where the news could be funny. (Even if I didn’t understand the humor, the laugh track showed that people were enjoying it.)
When I was a kid, the sitcom Mary Hartman, Mary Hartman came with a parental guidance warning. My parents watched it, but exiled me to my room because it was for “adults.” I had vague ideas of what this show was like, but I was generally convinced it had to be incredibly good. Years later I was disabused of this notion. It was okay, but it was a soap opera parody which didn’t land with me.
On the other hand, I did watch the spinoff Fernwood 2 Night (later America 2-Night.) a talk show parody from long before The Larry Sanders Show.
That was my impression when I finally saw the thing. I remember it being a very big deal at the time, as it was the first prime time network show with a warning. [EDIT: As @moviegique points out, MH, MH was syndicated, not on a network] Remember this was the old days when the only TV was broadcast stations from the three networks, PBS and one or two independents. Broadcast Standard and Practices departments (the “network censors”) were still a thing at the networks and the FCC paid attention. If they didn’t like something, they returned the script with changes. In retrospect, I wonder if it was mostly about an attempt to drum up ratings. I bet Norman Lear says something about it in an interview somewhere.
But it wasn’t a network show. The networks didn’t pick it up–really, an anti-cosumerism show was long-shot at best–and it ended up being syndicated (a fairly early example of this, I believe).
In L.A., I’m pretty sure it never aired before 11PM.