An identity almost definitionally can change because it's what someone identifies as. It's not necessarily transphobic to believe that, again it's all about letting people choose what makes them happiest!
It's also fine to think that being trans is more than an identity, but that's more of a theoretical or analytical (and complicated) discussion .
For political and simplistic purposes just allowing people to choose their identities has all the practical benefit we need.
Well I draw the line where they draw the line, if they say they're cis I believe them if they say they're trans I believe them. Easy as!