No, you're wrong: nobody is attacked for their 'gender identity' because whatever is is, it's something in their head: the reason trans males such as myself are attacked is because homophobic males view feminine males as inferior. It's rooted in homophobia, which itself is rooted in misogyny.
Not really. The point is you don't have to change your body to match your personality/
The dominant vector in transgender culture, what make's today's culture so different from the past, is that it posits everyone's 'gender identity' (that feeling by which one knows one is a man or a woman) is innate. There is a philosophical problem here in that none of us know how it feels to be anyone or anything other than ourselves: we are not a species of mind-readers.
The 'transgendered soul' is a belief, an ideology: all faiths, ideologies or beliefs are open to question, however should people be persecuted for their faiths? No. Note the Equality Act protects faith already.
It's a cultural identity, the effect though of gender as a cultural hierarchy means it's a two way process, and we are treated by others according to the rules of gender. We cannot escape this, as we cannot police the thoughts of others, so whether an 'agender identity' means something outside of the mind of the believer is very much moot.
The problem is that this won't happen because any approach other than 'gender affirmation' is being blocked. Affirmation has its own problems, it presupposes the etiology of trans is monolithic when it is not the case: the reasons a child may display a 'transgender identity' and the reasons a mature adult would do so, are fundamentally different. Treating these populations the same ignores this difference.
Yes, it needs an attempt made to make good law, the problem is law tends to be politically motivated and riddled with 'unintended consequences'. Solid legal definitions of 'male', 'female', 'sex', 'gender', 'woman' and 'man' would be a great start,