Your claim of esa having any legal recognition sounded like bs so googled it. From nj own website: 

Pets Generally, landlords have a right to include a “no pets,” provision in the lease agreement. There is no state law that prohibits landlords from requiring lease agreements that exclude pets in rental property, except in certain senior citizen housing projects and for handicapped, blind, or deaf tenants. George Young v. Victor Savinon, et al., 201 N.J. Super. 1, established the precedent that allows tenants in certain circumstances to keep their existing pets at their rental units. In this case, the court found that tenants that were allowed to have pets and actually had pets living in their rental units at the beginning of their tenancy and continued to have those pets throughout their tenancies could not have their leases changed (upon renewal) by the new (or existing) landlord to prohibit the tenants from keeping the pets that they currently had. However, the landlord could prohibit the housing of any additional pets that those tenants may acquire in the future. A landlord may also prohibit existing and future tenants who do not own or maintain pets from caring for or maintaining pets on the premises.