You are making a logical error here. Belief that one is a woman and expecting/forcing others to treat you as a woman are two different things. You can have either of them without the other.

The prison issue can be solved the same way the sport issue can be: "Prove it." However, society must recognize that trans women are particularly at risk in male prisons, and it is "cruel and unusual" punishment to place them there. Simply house them separately from both cis women and men.