Any Vampire Weekend fans in the house? Their first album, which had great commercial and critical success, has a whole lot of classical influence (Chopin, Bach, etc). They incorporated plenty of "world" influences as well (afrobeat, ska). I wouldn't say either of those areas of music are "relevant" to a lot of people, but Vampire Weekend certainly is. (they're my favorite band so pardon my bias).
I also love this quote from the writer Susan Sontag: "And I’ve certainly learned something as a writer from the way Schnabel plays Beethoven, Glenn Gould plays Bach, and Mitsuko Uchida plays Mozart." That's from an interview in 1995, and Sontag is most certainly a "relevant" writer. Tolstoy wrote a whole story named after Beethoven's Kreutzer sonata, Nietzsche cited Beethoven and Wagner plenty in his philosophical works, which continue to influence the cultural elite. And how about Kubrick's use of classical music in his films? Strauss in 2001, Penderecki in The Shining, Beethoven in Clockwork Orange. Personally, since the US 2016 election, I've been fascinated by the music of Shostakovich (composed under Stalin's totalitarian regime) and Wagner's operas, particularly the ring cycle (horrifically appropriated by the Nazis, but beautiful, wildly sensual music nonetheless).
Besides that, classical concerts in the US, and moreso in Europe and Asia, continue to sell out audiences in huge concert halls. The Metropolitan Opera's livestream of Renee Fleming's final performance as the heroine in Strauss' opera "Der Rosenkavalier" was the highest-grossing in box offices a few weekends ago. The Elbphilarmonie, a MASSIVE and extremely expensive new concert hall in Germany, just recently opened as well. There's plenty of evidence for classical music's continued relevance.
But more important than any of that, I think, is if it's relevant to you personally. Does classical music (whether it's Bach, Beethoven, or Boulez) make you feel something? Do you get joy out of it? Does it clarify things for you? Is it interesting to you on a purely intellectual level? Do you get joy from playing it yourself, or watching your friends or loved ones play it? That, I think, is what matters, not simply whether it's enjoyed by a large enough swath of the population or gets enough playtime on the radio. Regardless of whether it's relevant, it exists, the recordings are out there, plenty of people listen to it, it continues to exert outsized influence on modern popular culture, and we ought to seek as much enjoyment as we can from it.
