There are some vague indications of an "evolved sensibility," but in demonstration, these folks, whether it be Scotty, Tom Paris, or Tilly, are just character-types plucked from the time in which the episodes were written. Which is fine. It isn't about what century it's set it. That's just a dramatic convention, a tool, a backdrop upon which the story may reflect our current humanity. It's also about appealing to a broad audience. That's what I've come to expect from Star Trek and I think Discovery delivers that pretty well.
I agree that the main characters need to be relatable, so having them hew to modern social norms makes sense.
However, in the case of Discovery, the main characters were almost all 23rd century, even after going to the 32nd. The future was the "alien setting" for them, much as the Delta Quadrant was for Voyager.