The body odor must be intense.

Oh, there’s a fairly established market of fursuit cleaner/fragrances that are a mixture of alcohol and scent. Some of them smell really nice (think Bath & Body Works, not high class perfum). There’s also been a lot more attention given in the past decade or so to making washable suits. You’ll definitely get people who smell like an anime convention, but at this point it’s by choice and not because suits are uncleanable.