Gender neutral booking forms

I'm wondering if anyone has encountered gender neutral requests on their websites and what they have done to accommodate being non-binary.

We have had one customer request the use of the MX title and discussions are underway to allow this experience. However, I'm made aware of the back-end we have to classify people as either male or female due to third-party suppliers for ferries etc - I manage the UX for a travel website so as you can imagine we link with a lot of third parties.

Has anyone encountered this issue or able to offer related article links to this.