Self-ID

I was figuring out how much it would cost, and it struck me that I'd rather that my birth certificate said female - fulfilling Pippa's prophecy - while I'd rather have the 'x' marker on my passport. Overseas, I think that the 'x' thing is easier to explain, but in NZ there's definitely a lot of people that would consider me as a woman, and many that find that proposterous due to my body hair. Regardless, I'm sick of debating this. Every time that I attempt to change my ID, it's usually a massive hassle with extra steps that regular people aren't asked to do. For example, last time I wanted to change my passport to an 'x', I was told that I was supposed to get a Justice of the Peace to witness it.