"Is it our or your cat?"
Translation:Ist es unsere oder eure Katze?
Sure, but only if the noun has already been introduced to the sentence/conversation. As this sentence is presumed to stand alone without context, it's ok to use the genderless pronoun until the noun is introduced (even if it's later in the same sentence).
If it had already been established that we're talking about a cat, we would use the matching gendered pronoun sie:
E.g. Siehst du die Katze da im Garten? Ist sie unsere oder eure (Katze)?
For comparison: I'd also say, "Ist es deine Mutter oder deine Tante, die dich begleitet?" (Is it your mother or your aunt who accompanies you [at your wedding next week]?) or "This woman on this photograph - ist das deine Mutter oder deine Tante?", "Somebody / A woman is coming up the driveway." - "Ist es deine Mutter?"
To me, "A woman is coming up the driveway." - "Ist sie deine Mutter?" seems to stress the "sie" and sounds like I doubt / I'm surprised that that woman is your mother. Same as in English, I guess. "Is it your mother?" vs. "Is she your mother?"
It could be two couples talking. "Eure" is not necessarily a group of people, just more than one. So one neighbor couple (since it used "unsere") talking to another neighbor couple who heard that a cat was roaming the neighborhood and one of them said, "Ist es unsere oder eure Katze?"