FWIW, a personal response as a Kiwi.
This obsession that some of my compatriots on the left have with acknowledging transwomen as women is a bugbear of mine. It is one of things holding them back, turning people with similar worldviews to mine away from them.
That said, I consider the trans gender issue to be far less important than other issues. Make no mistake, I am a lifetime left wing voter. I have voted Labour at every election but one (where I voted Green with my party vote, but still voted for the Labour candidate).
I have never voted National/conservative, and I never will. They represent everything I despise - their elitism, their selfishness, their corporate greed, their bashing of the downtrodden with cruel welfare policies, their dehumanising of the poor, their derision for working families, their racist policies towards Māori, and their utter contempt for the environment.