I don't think the references will make it dated, but date it of its time. It's like watching Seinfeld; the show is very much of the 90s (having an episode about The English Patient, Ted Danson's plane, Kramer's mock-OJ chase, etc.), but since the humor was so well-done, it doesn't hurt things. If the humor around the references is done well (and so far it looks promising), then the references will become part of the fabric.
I agree to that. The difference with the Muppets here is that this is their first actual sitcom show, and sitcoms are very much the product of their time and will tend to be more topical. It's painful in animated sitcoms because it takes over a year to get an episode out there. Some Simpsons episodes come back incredibly dated before they even air. Sitcoms are much different than movies and specials, something the Muppets only had in recent years. As a sitcom they can make all these references and one off jokes and it still works a lot better than, say, The Crock Hunter parody (or general Scary Movie 3 before everyone hated them tone of the special) in VMX.
But I think a fairer comparison is with Sesame Street. The show has always been pop culture heavy and to me there's no difference between singing "Good Morning, Starshine," Grover parodying John Travolta to teach the alphabet, Miami Mice, or having One Direction with that one guy who left before the sketch even aired singing a self parody. SS has always tried hitting parody and celebrity as soon as they're relevant. Even recently, they parodied things that they actually missed the first time via sequels and movie remakes (Indian Jones, The A* Team, even Transformers). And often times the parodies are narrow or shallow. This is natural as it's a TV show with a decades long run.
Looking at The original Muppet Show, it's not like they were strangers to reference and parody. It was just a lot more subtle back then. They parodied Star Wars when it first came out, and then it became a cultural phenom and they had the actual droids, Wookie, and Mark Hamil. Some of it was dated, but held over okay despite some of the guest stars barely being relevant when they were on the air. Fast Forward to MT and you have a far more pop culture savvy show, and that was a mixed bag. You either got a clever parody like Seinfeld Babies or Co-Dependants Day (which both managed to hold up surprisingly) or...something with the pigs. Lets just leave it at that. From the looks of this new series, seems that it's toned down a bit and polished compared to MT. Definitely less in your face than the 2 made for TV movies. I don't mind the references to Uber and stuff as long as the humor can hold its own. And it looks like that's the case so far.