Greetings!
I was just watching an episode of All in the Family on DVD and was surprised when Archie Bunker said “god dammit.” That’s something that is not said/bleeped on modern TV. I know that All in the Family and Norman Lear tended to push the envelope, but for something to be OK back then, but un-allowable now seems odd, considering what the networks get away with today. When did the FCC change its mind?
Thanks
Aside from that episode of Family, when else was it ever used? 
Why do you think it’s something that is not said on modern TV? It’s so innocuous that it doesn’t even register.
One minute of Googling and I found this clip from It’s Always Sunny in Philadelphia: GODDAMN IT Supercut: It's Always Sunny in Philadelphia - YouTube - 6 minutes of the word Goddamn it.
It’s Always Sunny isn’t on broadcast tv
Always Sunny is on cable, which the FCC doesn’t control
I always assumed that it was the decision of the local television stations to censor this sort of thing to avoid offending a segment of their audience.
I will back up the OP, at least a bit. I have certainly seen cases where a character clearly says “Goddamned” or “God damn it,” and the “God” part will be cut out. Usually not bleeped, but just silenced. You can say “God” or you can say “damn,” but apparently you can’t say the two of them together.
It may be, as charmstr suggests, a local decision.
Once people stopped believing in god, it lost a lot of its steam as an expletive.
Or, we have much more shocking & controversial things to say these days and it’s considered kind of tame.
Or, you don’t watch the shows where they say it. Searching IMDB for “goddamn” in Quotes gives the following list, and this is just the first page:
American Horror Story
Breaking Bad
Boardwalk Empire
Orange is the New Black
True Detective
Suits
Dexter
Family Guy
True Blood
The Wire
South Park
In the late 1970s, I watched a network showing of Easy Rider. In the beginning Steppenwolf song, Pusher Man, they bleeped out every single “damn”, but left the “god” intact.
Totally weird sounding.
/end hijack
I don’t think any of those are on broadcast networks; they are all on cable networks. I do know I’ve heard “goddamn” on radio. I think the Don & Mike show had a booming (announcer voice) saying it on a regular basis.
Most of those are not over-the-air broadcast TV, so FCC rules don’t really apply. The only exception there is Family Guy, right? And they beep stuff on broadcast that they don’t beep in cable runs.
“Family Guy” is on Fox. I think you’re right about the rest, though. (I also am not sure I’ve heard “god damn” on “Family Guy,” either, but it wouldn’t necessarily surprise me.)
IIRC, after the Janet Jackson nipple Superbowl nipple incident, the FCC started cracking down on everything. Unrelated stuff, like risque comedy songs that they used to play on morning radio with impunity, were suddenly off limits. Is it possible that that’s when ‘god damn’ also became less acceptable?
No, “goddamn” was really never acceptable on broadcast TV. In the 70s, any movies that had it had the “God” part erased. Norman Lear pushed the envelope, as we would later say. Aside from the OP’s “goddamn”, AitF was the first AFAIK to acknowledge that toilets existed, with a well-timed flush acting as a comic rebuttal, and Maude called Arthur a “son of a bitch” (fully enunciated) at the end of a memorable episode. These were groundbreaking at the time.
In the 70s, radio removed all “heavy seven” words from songs (usually the “air play” version omitted them for you - see the 45 rpm version of “Who Are You”). Then in the 80s and 90s, the standards were relaxed. You could hear The Who ask who the fuck are you, and Steve Miller talkin’ ‘bout some funky shit goin’ down in the city, and Pink Floyd wanting no do-goody good bullshit.
But now, we’ve regressed. “They” are taking out all the offensive stuff again. Steve only sings about funky kicks goin’ down in the city, PF doesn’t want do-goody good bull~~~~, and The Who doesn’t know where the fuck their fuck went.
I recall an era when this was considered fairly mild TV-cussing and allowed, as the OP recalls. In the Christian Right '80s, even things like “Jesus!” were blipped or dubbed (or just not used at all). I have a clear recollection of a movie that used a very mild such blasphemy, a sotto voce muttering that was completely in character and in tune with the scene, and being a surprised and a bit shocked to hear it muted in the TV appearance of the film. Big movie; can’t remember which one.
But then, we’re still living with the fallout of the Reagan Right and Janet Jackson eras; I haven’t heard anything but the most tepid radio edits of rock standards in a long time. Makes me want to wear my Pogue Mahones t-shirt proudly, and on my next TV appearance. 
Ah, the 70s. When you could say “get your ass out of here” on TV ONLY if there was an actual donkey in camera view.
There is that. I hear “Damn it” a lot, but the Goddammit just seems like too many words… In IRL as well as on broadcast TV it seems.
Fun fact: I worked at a college radio station as a DJ for three years. We were informed that we could not say “ass” but we could say “bitch” or “bitchin’” so long as it was not directed at a specific person, and by extension “bitch-ass” for some strange reason was therefore allowed. They still advised against it since if we were reported the FCC would probably just decide it was generally profane and smack us anyway, especially since the station recently had a guy who went a bit nuts on air and got them reported already.
[Blazing Saddles paraphrased]You said nipple twice.
What world are you living on? Not even everyone on the SD has stopped believing in god. I assure you, there are a whole lot of people out there that not only believe in God, they’ll kill you for you not believing.