Your picture is tiny. It would help if you could post a few bigger pictures of the space as well as closeups of the countertops and cabinets.

Stone isn't dated. But murals and decorative insets over cook area are less popular now. That doesn't mean you have to choose subway tile. Without seeing a closeup of your countertop material it's tough to say, but I suspect people are suggesting "subway tile" because it's a simple material in a simple shape. But you could use ceramic tile in a different shape or layout. Stone backsplash tiles might work if your countertop isn't too busy, but if it has a lot of pattern or texture to it, the stone might fight with the counters.