Pixar: the Early Days a Never-Before-Seen 1996 Interview

Yes, the existence of the remakes is proof in favor of the continued relevance, not the opposite. Companies like Disney don't invest hundreds of millions (or more, if you count ancillary merchandising) in something they don't know to have an audience. Even when the films bomb theatrically, they make money in the long run through the "long tail" (VOD / home video purchases) and merchandising. So, yeah, the remakes are indicative of a continued relevance. Furthermore the original Snow White has a particular longevity since it was the first Walt Disney animated feature -- and the first animated feature in color. On top of that, it is based on the Grimm fairy tale which, though published in 1812, was likely in existence for hundreds of years prior to that publication. Per Joseph Campbell, stories like that have a continued relevance because they are expressing archetypal concerns; their value is not rooted in time, but in the unchanging aspects of the human psyche that remain relevant hundreds of years later.

So... yeah. Though there is a slight diminishment in the sense of its aesthetics, it objectively continues to be relevant, seeing as it was literally in theaters this year.