The stereoptypes are more annoying. Including a gay character opens up poptential for annoying stereotypes. Part of it is how common it is for gay characters to be in production compared to many productions of the past.
There are a few other limits I'd have that I didn't mention earlier, though some might sound more ridiculous.
I would not want any regular characters to have body piercings (besides earrings on women, and even then I wouldn't want them drawn unless when neccessary) or tattooes (I'm sure the animators wouldn't mind that; I'd expect that to be part to animate). I feel it's too common these days in real life.
I wouldn't want men or really hideously ugly women to be shown in revealing womens clothing. To me that's usually gross. Sure, I'd want women to frequently be seen in really sexy outfits for the sake of pleasing the young male audience (including myself) and to open up sexual harrassment jokes from other characters, but I only want to include my opinion of good-quality disgusting humor.
I really don't want any recurring characters to be killed off. It's okay for a character to die in his/her introductory episode, but I really am a character person, and don't want them to die.
I wouldn't want nipples to be drawn on men when not wearing shirts (I would obviously want them drawn on women, but we know the censors won't allow it). To me nipples on male cartoon characters usually look freaky (though not too big a deal on The Simpsons).
Not that it's common on animated sitcoms, but I wouldn't want there to be many long storylines that last several episodes, like most of today's live-action sitcoms. I wouldn't rule out occasional two-parters, and I might not rule out the occasional mini-storyline during a season (and I have thought of one such idea), but I want to keep most of the episodes self-contained.