I think the most obvious match to what you are talking about in terms of social psychology terminology is cognitive dissonance theory. This theory covers a lot of phenomena, but in relation to friendship an attitude formation, it suggests that we will tend to like what our friends like in order to achieve a state of belief consistency.
From a more sociological perspective, you could look into homophily. This is the idea that "birds of a feather flock together". But in addition to people being attracted to those similar to them, there is also a process by which such an effect emerges over time.
In general there many mechanisms that could describe the process of starting to like something because your friends like it.
- mere-exposure effect: Merely experiencing something can help you to like something.
- Persuasion, learning, etc: In general, a friend may help you to appreciate something. If its sport, they may explain the rules and communicate the finer points of strategy. If its music, the friend may explain the history of the style, the meaning of the lyrics, or the emotional importance of the music.
- Positive associations: Spending time with a friend whose company you enjoy will help to create positive associations with other things you do with them.
- Social norms: Spending time with your friend may create social norms that the things that they do are normal and appropriate.