Think about this from a different prospective. Many buyers choose co-op which are NOT pet friendly for the reasons mentioned above.
With that mentioned, there are a number of co-ops which are pet friendly, even in White Plains, lol, and I'm sure any realtor worth their commission will be able to find one for you.
P.S: I own a co-op...and two cats, Cheech & Chong. Contact me if I can be of additional service. (914-574-8220)