just as they are need to be more open minded of your liking anime, so should you be more open minded about their dislike for anime.
however, if they are making fun of you, and causing you discomfort just because they dont like anime, that is another situation. i would recommend talking about it, and telling them to stop because ANIME RULES - i mean, because they should be more mature. hopefully no breaking up is necessary.
but if you do break up with them, i mean, anime can be your soulmate <3