It really depends on how they choose to adapt the source material. At the time the film was released, ABBA had not yet experienced their resurgence in popularity. Muriel's obsession with ABBA supported her outlook on occasion, but more importantly, it defined the more nerdy and dated aspects of her character (particularly in Australia, which had a very rabid and short-lived obsession with ABBA unlike any other country). The only time a song was used in the plot was in the karaoke scene (or she'd sing a couple of lines). The rest of the ABBA music served as a soundtrack, but wasn't really relevant to the plot.
If the adaptation is set in the current day, I don't think her ABBA obsession would have to be utilized. It could be any cheesy pop group to which she feels a personal connection that would be considered currently outdated (though not as well known in the US, Steps would serve nicely as a substitute, having significant Australian popularity in the mid-90s). Or this particular aspect of her character could be highlighted in other pop culture references. ABBA really isn't necessary to the character or the story. It was just a clever device for the time the film was produced.
I do think this would be a difficult show to produce onstage. Those who aren't familiar with it could easily get the wrong idea that it is some sort of romantic comedy fluff piece and may be put off by its somber moments and overall poignancy.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian
