It is illegal to discriminate against people based upon age (there goes the babies and incontinent or clumsy seniors exclusion, unless the landlord wants to be sued by (and lose) the Fair Housing Administration.
Lots of landlords in college towns discriminate against Frat members. Many city ordinances disallow more than a specified number of non-related persons from living together. I think it is 5 in my city, and yes, they are very specific on what defines a relationship--I think up to 3 degrees of consanguity means related and more than that means not by our definitions.
It is not illegal to discriminate against pets. Regardless of whether or not chickens make less mess than some people, a landlord is allowed a great deal of latitude in choosing whom to rent to and whom not to. Most savvy landlords do a credit and/or reference check to see whether prospective tenants are likely to pay their rent, likely to cause the police to show up on a periodic or regular basis, are likely to keep the property in good repair, etc. A landlord cannot discriminate based upon age, sex, race or other protected rights, but htey CAN discriminate based upon a prospective tenant who does not pay his/her bills, who does not maintain the property (cleanliness and any other terms written into the lease), has a history of police activity, criminal record, etc.
As a prospective tenant, having a proven track record of keeping the property immaculate, paying ones rent on time and in full, will go a long ways towards having exceptions (such as chickens or other pets) approved by the landlord.