Loyalty: In addition to Male and Female, Delta includes “Unspecified (X)” and “Undisclosed (U)” as gender options on a SkyMiles profile. Delta also has a “preferred name” field to greet you on delta.com by a name that differs from the one on your documents; it’s unclear if this extends to in-person interactions with Delta staff.
Changing an existing gender on a SkyMiles account requires you to upload supporting documentation. (I uploaded a scan of the picture page of my passport.) The change appeared to take effect on my profile within 10 minutes.
Booking: The same Unspecified (X) and Undisclosed (U) options are included in the gender field when booking a flight.
Check-in: I have not yet attempted check-in with a gender X passport on Delta.
Let Me X Plane 