Does it make sexuality redundant if people can lie about their sexuality, or even change it? No.
But we don't change the way we treat people in society because of their sexuality (at least we shouldn't do).
The problem with 'gender identity' is that it has real, physical consequences. Less so for men, which is why it's possibly harder for you to see the problems. If all there was to 'gender identity' was a man, who one morning announced to the world 'I'm a woman today', and we could all just get on with our lives, simply thinking 'why did he need to say that?', as we might if someone had just walked in saying 'I'm gay today', there wouldn't be a problem.
But what actually happens, is a man puts on a dress, a wig and some make-up, announces he's a woman, and walks in to the women's toilets and changing rooms, making the women and girls in there uncomfortable. Why should his 'gender identity', which can change from day to day, be seen as more important than his sex, which stays the same?
A confused teenager, feeling out of step with other children of their sex, decides that it must be because they have an opposite sex gender identity. This is increasingly happening to teenage girls, who in the current climate end up on a conveyor belt of puberty blockers, cross-sex hormones and irreversible surgery. How is this comparable to a teenager realising that they are attracted to people of the same sex?