I would want to influence my kids music tastes but if they did like something else i would respect that too as long as they're not blasting total crap. Plus i wouldnt let them ever change my radio/cds when im home.
I grew up in a house where basically the only thing played was classic rock. My dad had it set so the "main radio" i guess i would call it came on automatically right around when he got home from work untill around 11 at night and its still like that. Now the only music i really like is classic rock so i would definately say peoples intrests can be influenced.