It seems to me we've got a few different worlds here. I say "worlds" and not "timelines" because this really does resemble something like DC's "infinite earths" rather than something like, say, Star Trek, which has done a stellar job of knitting every iteration of the show and movies together.
Off the bat, we have - The Muppet Show. It's what they're primarily known for, so we'll call that Muppet-Earth-1. Then there's The Muppet Movie, which is a movie-within-a-movie, but Kermit says it's "sort of approximately how it happened." I say we take the frog's word for it. So, the events of The Muppet Movie, while a movie, actually happened. We can safely put Kermit's Swamp Years in Muppet-Earth-1, since it does noting, far as I can remember, to contradict the events we see in The Muppet Movie. Same with It’s a Very Merry Muppet Christmas Movie, except that introduces an alternate reality. So we’ll call that one Muppet-Alt-Earth-1. And, since we’ve already seen The Standard Rich & Famous Contract in the trailers for The Muppets, let’s say that movie is in Muppet-Earth-1. This is the world where the Muppets are famous, Kermit is from the swamp, they all met on their way to become rich and famous, and Orson Welles was having a good day and gave a big group of weirdos an entertainment deal, which we can assume included The Muppet Show. Eventually they would move on to The Jim Henson Hour and Muppets Tonight.
Then we have the other movies. The Great Muppet Caper, The Muppet Christmas Carol, and Muppet Treasure Island are all fairly straightforward. They're just bigger versions of sketches. It's the Muppets putting on a show. In this case, making a movie. They went to the set, joked around with some human celebrities, and went home. They're all in what we’ll call Muppet-Earth-2. Fairly simple.
The specials don’t really present problems for the most part. The John Denver specials are just the Muppets on vacation from the movies and shows.
Good so far?
The Muppets Wizard of Oz is a tricky one because we get the Muppets from Muppet-Earth-1 – their real selves – putting on a show. But the stuff on Oz is all in Ashanti’s dream. Or was it a dream? I forgot. Anyway it’s not the real Muppets. It’s just them playing roles in Ashanti’s mind. So, we can call that Muppet-Alt-Earth-2. For fun, we can put the two Studio DC specials in there too, since I’m sure we’d like to think of them as imaginary. Again – Muppets’ Wizard of Oz gives us real Muppet-Earth-1 Muppets, and then Muppet-Alt-Earth-2 Muppets. We decide to mostly forget the latter, and since Muppet-Earth-1 Muppets don’t even know there are Muppet-Alt-Earth-2 Muppets, everyone is happy.
Now we have The Muppets Take Manhattan. This maybe presents the hardest part of Muppet continuity to pin down. Here’s what I think. Just because you’re famous in movies and TV doesn’t mean you can just go become a stage performer. In an attempt to broaden their horizons, the Muppets take some time off from being Rich & Famous to go to college and get their BA in Drama. They do, and then try to get their show off the ground, but Orson Welles is a little more senile now and isn’t around to help. But, of course, luck and perseverance lead to the success of our friends yet again! They perform their show, likely win a lot of Tony Awards, and also two of them get married.
Then things get difficult. Not difficult to understand, necessarily… but difficult to accept. Muppets From Space and Letters to Santa all present a somewhat contradictory world to Muppet-Earth-1. In these, the Muppets *gasp* are not famous!!! In Muppets From Space, they live in a boarding house and seem to have mostly retired from show business, except for the occasional Bat Mitzvah! Or was it a Bar Mitzvah? Who cares, the Muppets aren’t famous! In Letters to Santa it appears the mortgage for the boarding house was too much and they moved to an apartment complex in New York.
SO WHAT HAPPENED???
Well, pretty much what happened in real life. Muppet Treasure Island and Muppets From Space and Muppets Tonight didn’t do so hot. Our Muppet-Earth-1 Muppets were forced to not have TV shows anymore, and people don’t seem to really know who they are in Muppets From Space. We know this because Katie Holmes asked Clifford if he was some kind of alien or something. Or something. Ha!
And, at some point, we can safely – and sadly – assume that the Muppets decide to go their separate ways, as we will see at the beginning of The Muppets. Gonzo goes back to plumbing, Kermit and Piggy probably get divorced (or separated?), and Rowlf sleeps in a hammock.
And then…?
We’ll find out.
Then there’s Muppet Babies. Which was a cartoon someone made about the Muppets being babies together. Since it isn’t the Muppets playing characters, but a group of animators, we shall call it… Muppet-Baby-Earth-1. I guess.
There you have it. Muppet continuity in a very complicated little nutshell.