I vote no. Leave it to a plugin.
If there were one I'd like to put my true identification which is none of the above listed. I identify as a "Rainbow Princess Unicorn of the Fourth Order" in which I would feel both left out and angry because my identification isn't listed there.
I feel that this is a niche need and therefore needs a niche solution. Plugin. Plugin. Plugin.
Edit: To be clear I joke because I believe that this opens up a pathway for people to attack others because of their gender preference. I have removed gender options completely from my community and people can choose to identify in their introduction, in their about me or not at all. It is up to them to make that choice, not me.