I don't think that this is true in many cases, especially with classic animation. Pinocchio didn't feature pop culture references, but its sense of humor was exactly in line with its era. Other contemporary Disney films--e.g. Fantasia, Dumbo--featured things that are exceedingly 40s, especially with the racist caricatures in both of those films. Besides the parts that have grown offensive over time, the movies still hold well just because they are very well made.
Contrast to Looney Tunes, which certainly used all sorts of pop culture references and even outright parody (Bugs Bunny eating carrots was a spoof of a famous 30s film), and fares about the same. While those shorts are certainly products of their time now (and there are PLENTY of morally repugnant shorts from the Merrie Melodies roster), the best of those are basically eternal classics just like Disney's films. Maybe the references fly over modern audiences, but the jokes sure still land.
A similar transformation is happening to the 90s era Disney films, but more importantly it's already happened to the 90s era WB/Spielberg cartoons--Tiny Toons, Animaniacs, Pinky & the Brain, et. al. Those were and still are considered some of the best of all TV animation, but they were also jam-packed with so many pop culture references that sometimes you need an encyclopedia to get the jokes now even if you were alive at the time. But even with that, they haven't aged POORLY; they're still just as good now as they were thirty years ago.
I guess none of this matters that much to the topic of this Raya movie, but I am betting that it's no more contemporary or wacky than Aristocats was in the 70s or Mulan was in the 90s. And if it's good, it'll age just as well as all other Disney movies in 20 or 30 years' time.
The only Disney animation movies I've seen in the past many years are Zootopia and Wreck-it Ralph, though, so maybe timelessness isn't really something that's ever crossed my mind anyway lol