There's this girl. I really don't know if she likes me or not, but I think she did at first. Then we talked about things... do we like kids, do we like country music, do we like dancing, do we like movies... and basically all her interests are the opposite of those. I think the more she realized this the less flirty and romantic she got. I guess I wouldn't want to be in a relationship with her either even tho every smile and every word makes my heart skip.
If you're willing and open to explore your interests together and teach each other new things, then yes you should stay. But if you guys are repulsed by enjoying new experiences together and you want to live separate lives, then break up.
So here's why it depends: The only way a relationship of opposite interests works is if you have an appreciation for their interests. For example: I love to write music. My boyfriend doesn't love to write music. But he supports both my music and my song writing as well as my dreams. Another example: A girl loves country music but the boy hates it... Yet when she gets in his car he turns on the country station appreciating that that is what she likes and understanding that it'll make her happy. If you can't do these compromises for each other then you can't be together.