I don't think I could ask someone to give up certain types of music, or TV shows, movies or books. If they are a Christian, they have the Holy Spirit to convict them and encourage them to make the right decision. I hardly ever listen anymore, but I do listen to some secular music. When I do, I look for the ones that are uplifting and inspirational, rather than about drugs/money/sex - none of those songs ever appealed to me. If you're both adults (or even teens), then you're old enough to make your own decisions and someone pressuring you to give something up will only make you feel like you're being parented - not good for a relationship. There are types of music that I wouldn't listen to, but I know others who do. And, there are books out there that I feel led to stay away from, but many of my Christian friends read and love; I don't judge them for it, or criticize, because I know the Holy Spirit does brings conviction to each of us, and I know that there are things that I have an interest in (and I have prayed about, so I've already had the discussion with God over them!), that would get eyebrow-raises from people I know. But, I made the decision on my own, and it is a decision that I made after I sought God. So, to each his/her own. No, I would not ask someone to give something up because it wasn't "Christian". I watch movies that are secular,watch TV shows that are secular, read books that are secular, and listen to music that is secular. The question I ask myself does, "Does this dishonor God?" I had music that I had gotten years before I accepted Christ that I did toss out a while back, because when I asked that question, the answer was "Yes." But I have other secular music that stayed. Same with movies, TV, and books.
There are a lot of things that the Bible doesn't specifically tell us we shouldn't do, which is why seeking God and listening to the Holy Spirit is so important. I had a friend once mention that perhaps the Bible is silent on certain issues just so that we would learn to use discernment and to seek God on such matters. It's another factor of spiritual maturity. Think about it. When we are young, our parents make decisions for us - what we're going to wear, what we're going to eat, how we manage our time. We know what to do, because we're told what to do. But, as we grow and mature, we have to begin to make these decisions for ourselves, and learn how to make the right ones, understanding that there are consequences when we make the wrong decision.
I wouldn't say that wanting someone to make changes in the music they listen to is necessarily selfish, as I have noticed that those Christians out there who do criticize the tastes of others really do have their best interests at heart - they do believe that such music or other forms of entertainment are sinful. And, of course, GIGO (garbage in, garbage out) - what we take in affects us as people, so we must be careful not to feed ourselves garbage from the world. But, as I said above, even though they are well-meaning, it comes across as judgmental and parental, which will only serve to make people resistant to what is being said anyway; we tend to become defensive when someone is trying to make decisions for us, when we are quite capable of making them ourselves.
I make my choices, and do my best to let the Holy Spirit guide me. And, for those who are into things that I wouldn't necessarily be into, I pray that God will guide them as well. We're all going to disagree on things, whether it's forms of entertainment, or whether we should celebrate Christmas and eat meat. I point people to Romans 14 (which discusses eating meat and celebrating certain days, lol - so those weren't random examples I threw out there) when something like this comes up. In the end, it is not the opinion of other people that matter, it is the opinion of God that matters.