If a participant doesn’t want to answer the questions, provide a way for them to communicate with you to find out more about the reason why.
Design the survey to ensure there are available options for all participants, beyond the more common-place answers. For example, a gender-neutral or non-binary participant may experience distress or not complete the survey if there is no valid option to choose from an answer list.
In this case, where there are various shades of gender identification, it is difficult to know all of them, or include all variations in the survey answer options. A simple way around this is to provide an ‘Other’ field, in which participants can write an answer of their choosing in a free-text box.
If you do not want to allow for additional answers, you can always include a ‘Prefer not to say’ or ‘Do not want to answer’ option, so that there is an option for opting-out of mandatory questions.