Visa WaiverESTA does not currently have a gender "X" to choose from on the application. It is suggested that the traveler choose from whichever they feel most comfortable. ESTA will not be denied solely on the gender chosen on the application.
Completing Your ESTA Application
A travel authorization is valid for two years after the application date or until the passport expiration date whichever happens first.
If you obtain a new passport or change your name, gender or country of citizenship, you will be required to apply for a new travel authorization.
If your ESTA has expired, you must reapply by submitting a new application.
Your ESTA must be valid when you enter the U.S., if it expires during your stay it will not affect your departure.