Caveat: IANAL and just thinking aloud.

I don't think the ADA is broad enough to be able to ban pet-friendly workspaces. PFW can arguably be good for mental health depending on implementation. Plus, mandating "no potential allergens" would have to include scents, food, etc https://twitter.com/ElGranSenglar/status/1381351250353082370

(ngl I personally wouldn't object to banning perfumes, but probably unlikely)

The ADA does (theoretically) mean someone with an allergy has a right to an allergen-free environment. In practice this probably means "uh I guess you can work from home, dunno, accommodation is hard"

There's also the matter of clashing ADA rights when one person uses a service animal and another person has allergies. Banning PFW would reduce but not eliminate allergy conflict.

All that said, given how hard it is for people to get actual ADA needs met, I doubt a blanket ban on something that's only potentially ADA.

(Not wanting to be around other ppls' pets is a valid personal choice! Pet policies are complicated!)