Read the lease agreement carefully, exotics can mean anything, any animal not native to your state even. offer to show the landlord the animal, and the enclosure it will be kept in.
and there is no reason to risk eviction for your pets. moving is expensive! talk to the landlord, be honest. it was hard for me to find a place to rent with all the animals i have....try finding a place to rent with 4 dogs! but i did. and it's actually a great place and i have an awesome landlord. i also have an airtight lease that lists EXACTLY what the pet policy is. I am allowed to have reptiles, dogs, cats, fish, and rodents. i dont have birds, so i did not even bother asking to add them in...
the main reason landlords ban snakes is for one reason....snakes can escape! and can cause damage especially if they find their way into the walls and plumbing. and also, it really is not cool for a landlord to find "Fluffy" long after a tenant has vacated......
the shelter has had to pick up stray snakes or illegal snakes from tenants, usually the snake is big, and/or has not been properly housed. and i've taken in snakes from people who tried to get them by their landlord and nearly got evicted for being dishonest. the landlord even stated "if you had only ASKED before you signed the lease I MAY have considered it!" it's the principle of it all too. who knows what else that tenant may lie about next...how many people they have living there, any other animals they may try to sneak in...etc.
and there's also the issue of what snakes eat. some people feed their snakes live rodents that also can escape or they dont clean up after the rodents and THEY STINK! rodents are messy critters. i have a hamster and oh man, i have to clean his enclosure at least once a week if i fall behind, he can reek!
and it does suck, but it only takes one irresponsible tenant to burn a landlord and ruin for the rest of us responsible people. i've talked to landlords who used to allow pets but would not allow it again because of all the costs they incurred in repairing the damages from the previous irresponsible tenant. I actually got very lucky, my current landlord did get burned by a previous tenant who owned a dog that tore up the place...i talked to them, they met my dogs and other animals and with an awesome reference from my previous landlord they allowed me to rent from them. They were so impressed with the care of my animals and of their property that they asked me to renew my lease for another 16 months! I did. Even though they got burned, they still were willing to give me a chance. It did take some work on my part though to prove they could trust me.
It will take some work, but you might get lucky and find a place that will allow your pets.