Honestly... I don't know. Disliking someone's animals is kind of like disliking _them_, for me... But for some people, it's not like that. Guinea pigs could be dealt with - put them in their own room, or something like that. A dog or a cat? If they can't live with the big, cageless animal, it's a no.
My brother and sister-in-law almost didn't get married or even date because at first, he didn't like her dog (of course, now Mei has her own couch, tons of toys, and my brother built a special drawer for the remotes so she won't chew on them because "she doesn't know any better, she's only a little dog!" XD). In my situation, my boyfriend has HORRIBLE allergies and asthma. Whenever he comes over to my apartment, he's always sneezing and wheezing. Even still, though, if I'm out of town, he'll come over and hug and snuggle my piggies and give them their daily doses of love, feed them, refill their water bottles... the works. He knows I love my piggies (we call them "piddos" for some reason XD just a weird, affectionate nickname for them), and he knows they're very important to me. I mean, I *love* having extra money to spend on books and video games, but I'll go into debt to keep my little piddos happy!
So, I don't know. You'll have to handle it in your own way. What my boyfriend and I did was move things over to his apartment (like the cable internet and TV), and just spend our time together over there. Or we stay out in the living room, since the pigs are in my bedroom. Even still, he'll go into my room to say hi to the pigs... I can't believe him, sometimes. He's allergic to either them or the hay, but he loves them! He's always cuddling Pumpkin when he's using my computer ^.^
You'll have to handle it your own way, but for me, (FOR ME - I'm not saying break up with him!!) I couldn't be seriously involved with a guy that was against having a zoo for a home ^.^
Currently, we only have fish and guinea pigs, but next come sugar gliders! XD