The old masters spoke to the world
I've never met a musician who didn't appreciate (if not enjoy) classical music. Even punk musicians appreciate classical music. It's layered, addresses emotion, it's BIG. It was an era where a precious handful of people were so honking creative and fabulously capable with the instruments that it produced a sweeping array of sound that affected the entire world.
In all the centuries since, very very few artists have attained either the popularity or the recognizability of the classical masters.
Will everyone on a space ship prefer classical music over, say, classic guitar, Jazz, blues, country, Acid... That's unrealistic.
But if it was the only music available? Some would get bored with it, but honestly, humans get bored all the time. How many of us float through our day permanently wired to our tunes? My own playlist is about 200 songs long and there are days that I'm sick of listening to them.
But, ignoring the question "why couldn't you bring other music along?" (by the time we're sailing through space in elegant starships the Beatles will be in the public domain), why only classical music?
Even at it's most explosive, it's not raucous. You can't really head-bang to the 1812 overture. I mean, you could... There's cannons, after all... but it's just not the same. You can't lose your self control to classical music like you can other genre.
It's rarely played loud. Some people are more interested in the beat than they are the melody. These are the people who, despite their car windows being up, can be heard a mile down the road with enough force to pound nails into the asphalt. I've had days when I turned the volume of classical music up, but to claim that it's loud would be a lie. This is important on a ship where you will meet the same small group of people every morning for breakfast for months if not years.
It's common to us all. Humans tend to find things that divide us ("I'm a little bit country... I'm a little bit rock-and-roll" sang Donny and Marie Osmond). Classical music is such a common part of our shared heritage that it tends to have a binding effect rather than a divisive effect (my perspective). How often do you see biker-vs-cowboy fights in the movies? OK, how often do you see Bach-vs-Mozart fights? You get my point.
And, last but in no way least...
The captain likes classical music. We like to think that the world is a democracy, but starships aren't. ("This isn't a #*@%! democracy!" screams Matthew McConaughey in U-571.) And if the captain loves classical music, then you better keep our ipod full of Reggae and Bubblegum Rock under your pillow.