Loyalty: JetBlue only lists Male and Female in the gender field on a TrueBlue profile. The gender field does not have to be filled in when an account is created, but there is no way to unset it once either Male or Female is chosen.
Booking: Only Male and Female are listed in the gender field when booking a flight.
Check-in: I have not yet attempted check-in with a gender X passport on JetBlue.
Company response: I have not yet contacted JetBlue about this.
Let Me X Plane 