Business owners in certain circumstances can be held responsible as it is their responsibility to keep the public safe on their grounds. (chicagopersonalinjurylawyerblog.com)
Dog breed discrimination is wrong, and breed ban laws do not keep the public safer. (bestfriends.org)
Since this does not serve to punish them, but simply keep the public safe, there is no prohibition against such a requirement. (law.stackexchange.com)