I found this clip via Mark Evanier, who found it via Lee Goldberg, and maybe somebody will now find it through me.
Anyway, this All in the Family clip was not intended to be aired, and I don't know what occasion it was made for -- it seems like something that might have been made as entertainment for a meeting, or something like that. It was made in 1975 when the FCC was creating the "Family Hour," a legendarily stupid decision which fascinates me and which I wrote about a couple of years ago. All in the Family was one of the shows most affected by the Family Hour, as I said in the previous post; the new rule forced it to leave the 8 p.m. timeslot where it had done so well, and several years later, it became more kid-friendly when it was moved back to 8 p.m. (the Family Hour rule was gone, but not the idea that 8 o'clock was for kids).
So in this clip, the Bunkers and Stivics clean up their manners in a Family-Hour-approved way, and then they gather together and sing the theme song with new lyrics, about all the naughty stuff that the Family Hour seeks to banish. Interestingly, the lyrics mention vasectomies, which hadn't actually happened on All in the Family yet, but did happen on the show a year later.