Sure! There are people composing classical music today, but you can sure, untill they are dead, main stream society won't give two good flying !@#$% about them or their music! That's not a assumption, thats a fact!
Actually, that
is an assumption, not a fact. There are mainstream living composers, though it's true probably the most mainstream classical compositions are film music.
Again you "assume" that because classical music has been in "OUR" society that it will endure into the future, when you really have no basis for this fact! It could be polka or gangsta rap!(God forbid!) for all we know!
Look, have you seen the episode "Suddenly Human"? There's a scene in that episode where a human teenager named Jono is up listening to loud pop music. Go watch that scene - the music that Jono, a being from three hundred years into the future, who grew up among aliens, listens to... well, it sounds painfully 80s, doesn't it?
This is precisely the problem. The greats of classical music can be added to but for the most part are largely constant, they don't feel dated because even when the episode was made they're hundreds of years old. Pop music is considerably more fickle - if there is anything that's going to still be listened to in centuries, it's really anyone's bet as to what. (The Beatles maybe? There's a conservative guess.)
All we could say for certain is that there will be new forms of pop music. We have no idea what they'd sound like, and any attempt by us to replicate it will probably sound dated a couple of decades from now. Another non-Trek example is the music of the Krell in
Forbidden Planet, compositions by a super-advanced alien race... which sound like the experimentally electronic score of the movie, which is primitive by today's standards, to say nothing of the staggering heights of civilization this alien race achieved. So it's perhaps best not to stray too far into this area, and there's the added corrollary that we don't know what or if pop music of the present will have a role in the future.
So, just as having your future characters talk about
Hamlet is a safer bet talking about
The Dark Knight, classical music is a viable constant. That's not me even claiming that it's better, just that it has a later expiry date.
As to what's considered classical music... making music old doesn't make it classical. Which is why I brought up the music hall hits - and even older, folk music. However there is a longstanding tradition of adapting and blending forms of popular and classical music, from the Hungarian Rhapsodies of Brahms to George Gershwin's compositions to even modern classical renditions of the Beatles and other rock groups. It's entirely possible that elements of rap could be incorporated into classical works (and may have already been done so, though I'd be ignorant of that.)
Oh, and I don't beleive you when you say you don't drink!
Teetotaller. Never touched the stuff in my life. I down inordinate amounts of caffeine and have dreadful eating habits, but hey, I don't drink alcohol.