You have no legal right to have a pet in an apartment. Pet owners are not a protected class. If the landlord is willing to accept pets, they can decide what fees/deposits they are comfortable with. There is nothing in any "act" that prevents a landlord from charging as they please for pets.

Pets and pet opwners are not a protected class unless the pet is required for use by a disabled person. As far as I know there are no laws regarding how much pet rent can be charged but deposit rules could come into play. Some states have rules on the amount of max deposit that could be asked for and some states have laws regarding non-refundable deposits and some do not. California for example is set up where a landlord can not charge any form of a non-refundable deposit, however, in Colorado you can. California also has it set-up where the maximum deposit can only 2.5 times the normal monthly rent.

The best thing to do.. check your local and state laws, and then, if you dont like the pet polices, dont rent there.