We have a customer who has a check payable to "John and Sue Doe Revocable Living Trust" of which he and his wife are trustees. He is requesting to open a joint account in the name of John and Sue Doe and deposit the check payable to the trust into that account. Should we allow them to do this?

No. It should be deposited into an account titled John & Sue Doe Revocable Living Trust. As trustees, they can then write a check out of the trust to them personally if that is what they want to do.

Agreed, the trust is a person. John Doe is a person. They are not the same person.

Your bank would not only have knowledge of the breach of fiduciary duty, you would have facilitated it.