Giving your life to Jesus was the most important decision you will ever make, and I'm thankful you've started on this new path which is God's path. Now make it your goal to stay on His path, by seeking His will for your life every day. The Bible says, "So then, just as you received Christ Jesus as Lord, continue to live in him" (Colossians 2:6).
Parents and teenagers often disagree about music and I've discovered that no matter what I say about it, not everyone will agree! But I suggest you begin by asking your parents what concerns them about your music not to argue with them, but to understand them. You still may not agree, but if they have some legitimate concerns, you should respect them.
Then ask God to help you be wise about the music you listen to (and not just music, but all forms of entertainment). Do some of the lyrics attack God or the Christian faith, or even exalt Satan? Do some promote immorality or other forms of behavior that displease God? Let the psalmist's commitment be yours: "I will have nothing to do with evil" (Psalm 101:4).
In addition, let me encourage you to become familiar with contemporary Christian music. It includes many musical styles, but they have one thing in common: They seek to point people to Jesus. The Bible says, "Set your hearts on things above, where Christ is" (Colossians 3:1). Make this your goal.