Do speakers choose your music preference

I definitely think there is something to this.  In my experience you need a decent sized woofer to give the right punch and energy above the deepest bass.  A pair of bookshelf speakers with a sub can sound almost indistinguishable from large floorstanders on small scale, unamplified music or relatively clean sounding pop.  I've never found that configuration satisfying on orchestral music or full-bodied rock, though.  It can't pull off the dynamics. 

I also think there are some tradeoffs between the ability to play loudly and the ability to sound right at lower volume.  Of all of the speakers I've had I've never had a pair that I thought really excelled at both.  I'm guessing that in order to play really loudly without distortion drivers need to be built more heavily, with more mass, and that extra mass doesn't respond as well at low volume as lower mass drivers do.  Whatever the cause this has been a tradeoff I've noticed consistently.

My ears hear a proper speaker as  one that simply produces good music, like an amp.

Genre specifc gear? Purely subjective. 

Was about to write no, speakers haven't driven it. Yes Moabs make classical sound so doggone good you just can't get enough of it. But they do that for rock too. And jazz. So was going to say they don't drive it, not like I go out shopping for music just because I know it will sound fabulous on these speakers. 

But then, wait a minute. Didn't you just pay a small fortune for a White Hot Tchaikovsky and a One Step Patricia Barber? Not the kind of thing I would have done before with my other speakers. So yeah, maybe, a little.

Other  way around.

Remember hating JBL 100s (boom boxes) 40 years ago.  That was reflective of my tastes in music/speakers then and continues to now (not that I don’t listen to some rock and really like bass sometimes). 

I think not only do speakers choose what sounds best on your system, but also your room does too!
How many folks are going to be able to play Stadium size rock concerts in their tiny den with little speakers employing 4" drivers and do that music any kind of justice? Same goes for large concert hall venues trying to be reproduced in a similar setting/speaker. OTOH, if you have a huge room with large floor standers that can drop down deep into the bass, then the ability to portray large scale will definitely be there--but maybe not intimate sounds? I think speaker manufacturers well know this...