It's interesting to think about how 'dateness' is difficult to define consistently, and may in fact lessen over time. For example:
I think Rent already sounded dated when it premiered, so I guess it hasn't got worse over time. Maybe it should be rewritten by some modern 'visionary' to be sent in the 70s, or whenever it was that that score would have sounded like modern pop/rock.
But in another 100 years no one will notice/care that the music isn't quite period-accurate, so the show will become less dated over time!
My Fair Lady may not have been any more sexist than certain contemporaneous shows, but the creators adapted an ahead-of-its-time play and added a sexist ending, which makes the musical seem dated when held up in comparison to its source material, IMO.
Kismet arguably seems dated now, given the rather blithe approach taken by its Western creators in depicting an Islam-influenced culture, but maybe that's a passing phase. Perhaps in fifty years when Islamic-Western relations have improved (we can hope), we can all laugh at/with this show together. (I'm not basing this on any concerns raised about specific modern productions of Kismet, but I imagine they would be inevitable if the show were given a major revival today.)
As to what (if anything) should be done about dated shows when putting them in front of modern audiences, I'm in two minds about all this. I can come up with many reasons for editing shows, but as soon as I imagine a self-important director taking the knife to one of the shows I love, I become cranky and feel as though they "just don't get it". The ideal approach would probably be pluralistic: let companies put on edited/adapted versions (if they obtain permission from the rights holders), but also license the original versions for companies which wish to produce them, and don't automatically demonise companies who choose to do so.
Editing a show may not always be about making modern audiences feel comfortable; it might be about ensuring that they focus on and get the full effect of certain worthwhile aspects of the show, rather than being distracted by "Wow, social attitudes were wacky back in those days" as the main takeaway of every other revival (unless that is indeed the point of a particular show). There's a place for replica productions of shows for anthropological reasons, but not every revival of a 'dated' show should be relegated to that purpose IMO. Many of us here are so familiar with classic shows that it's perhaps relatively easy for us to take the bad with the good, and to appreciate the 'anthropological' aspects of watching a dated show; but audience members who have paid substantial money to imbibe a show for the first and last time may find the dated aspects more distracting than we would predict. Theatre is about, among other things, communicating to the audience that you have in front of you here and now IMO.
OTOH, no doubt many a director has used similar arguments to completely desecrate great shows. There certainly is an argument for instead trusting audiences to weather the shock of the dated aspects of a show while simultaneously appreciating the show for what it was (and still is). People do seem to manage that for films such as Breakfast at Tiffany's and Gone With The Wind. Maybe people are more accustomed to seeing variant adaptations and other creative liberties in live stage works, so they're more inclined to wonder why dated lines aren't just cut or changed for the stage. Or maybe they feel more 'complicit' in viewing something offensive being portrayed onstage as compared to watching a period film, given that there's a real actor onstage seemingly asking for a laugh from the audience for a racist joke or whatever.
TBH it probably comes down to this for me: when I like changes to 'dated' shows, they're artistically justified, and when I don't like them, they're a betrayal of the original piece 