I mean personally, I loathe Pepe. I hate him for some reason, but meh... I'll live.
Well, to me, it's kind of like Pepe is to the Muppets as Elmo is to SST.
They're both kind of the new kids on the block who suddenly get a lot of attention, and become a part of the core group so fast as if they've been a part since the beginning.
Yes, I am aware that the red monster was around since the beginning, but the character of Elmo (that we know) didn't really surface until the 80s, and didn't really hit his stride until the 90s. It's almost the same with Pepe, have a bit of a mediocre part of MT, but then after a while, became a part of the group, and now it's kind of hard to imagine the Muppets without him, like for some these days, it's hard to imagine SST without Elmo.
But in all honesty, I'll take Pepe over Elmo anyday.
Now, getting back to the subject about the characters seemingly mellowed and watered down as of late, I think it's just the opposite with Pepe, in fact, compared to the other characters, he's rather "raunchy" - still being a kid at the time, I was shocked he said "It's going to suck" in IAVMMCM, because when you're a kid, to use "suck" like that is almost as bad as saying a swear word (at least with my old-fashioned parents who sheltered me greatly that I had to learn what things like sex and masturbation are through school). Then last year when he was on Craig Ferguson (ugh), and Craig asked him what he liked best about women? "Breasts", Pepe replies without hesistation. Even talking about some footage he's watched from like the Discovery Channel or something about the aquatic world, he found to be "Scary as h-e-l-l!"
When I think about it, in a way, it's kind of like something Jim tried to avoid from the start - being typecasted as strictly a children's entertainer, and because puppets are usually aimed at, and are associated with children, my thinking is that these companies who end up buying them try to make sure they're as "kid friendly" as possible, even though I wouldn't consider a movie like IAVMMCM to be completely kid-friendly (I mean, would you want a little kid to see Scooter cage dancing?) Jim always tried to make sure the Muppets could address all audiences - clever wordplay and banter that grownups could laugh at because they actually get it, while the kids would laugh simply because of the absurdity of it all... but maybe that vision has drifted away, and again, these companies are trying to make sure the Muppets are aimed mostly at children.
But again, there's still aspects that haven't been completely softened down and such, and again, I believe Pepe's a fine example of that.