People are going to like different things. Just because you do not like something does not mean other people should not. People are allowed to disagree with each other. Again, as I have said in the past it is part of something that makes us human. It would be a boring world if we all liked the same stuff. If everyone was the same, most of the creativity in the world would be gone.
If people like to watch romance movies, that's fine. It's not my thing, but if that is what they enjoy more power to them. If you hate romance movies, and thing they are the stupidest thing in the world, that's fine to.
Now the crucial thing to understand is that just because you think romance movies are stupid, does not mean that people that like romance movies are stupid. They are just different then you. You still should respect people with differing opinions.
Now a big problem with my whole argument here is that, if you think people who like romance movies are stupid, that's your opinion and you are entitled to it. However, you should still show respect for that person despite their differing opinion. You can argue with them, and try to convince them of your point of view. But you should not get vulgar or insulting about it (calling them stupid or a dork is not likely to convince them to take your side).
The only place where I can really see having conflict over differing opinions is when someones opinion is harmful to others. If it is your opinion that beating up old people is cool, there are likely to be issues (although if you really think that, but do not really act on it, you won't face the legal consequences of said opinion).
I guess my main point here is that it is good to have likes and dislikes. Yours will not always line up with other peoples. That is fine, that is normal. Now if you are friends with that person, then that just may be something you don't do together. If you are not friends with that person, then you really do not have to hang out with them or deal with the fact that they hold whatever opinion it is that you disagree with.
If you really care for a person that has differing opinions then you, then you really have to learn to deal with the fact that people are going to disagree. It might be you decide not to discuss that topic because it will only lead to bad arguments. It may be you have to do things separately from time to time. If it is something really as trivial as they like movies, or books, or games, or collecting something that you think is dumb, if you really care for that person you should encourage it anyway. Maybe you do not understand it but it makes them happy. If you care for them, you should want to see them happy.
Opinions. Everybody has them, and that is OK.