Liberty have come out in support of self ID: www.libertyhumanrights.org.uk/news/blog/have-your-say-gender-recognition-act-%E2%80%93-and-change-hundreds-thousands-peoples-lives-better
Their statement contains a particularly problematic statement: "If you aren’t trans, updating this Act will barely affect you at all."
I've been a member for years - I will have to leave over this.