If I want to back out of selling my house once I've accepted an offer with interest money can I since they have an exotic pet and my neighbors are unhappy?

If the contract has been signed and you have received a deposit, you drop out, you can and probably will be sued either to force you to perform the terms of the contract (sell the house) OR for the buyers' expenses and inconvenience.

Most likely no, if you try, the buyers will sue you, they can either force you to sell or you will pay for all the damages they have or may have because of this.

If your neighbors are not happy about some future pet this is not part of the purchase.
Will the neighbors buy your house from you to keep it from these people. Perhaps they will be willing to buy out the new buyers. It is often easy for people to complain they don't like something, but let see if they are willing to open their wallet or do they just want you to take the loss. If so, not very good friends.

Is this exotic pet legal to possess in your location?