I'm pretty liberal, and very trans-supportive, but there are literally two genders. It's an observable, measurable fact. To be honest, I feel like demanding that the word gender be redefined, rather than coming up with a term such as gender identity, is intentionally looking for an argument.
I don't believe that this helps trans folks, or people that do not self-identify in a strictly gender-binary manner. There is nothing to be gained by rebranding already existent words, and then telling everybody that they've been using those words incorrectly. This only hampers people's understanding and acceptance of trans and nonbinary people, and gives bigots a foothold by allowing them a scientifically valid talking point. For whatever reason, this always segues into "since gender is biological, transgenderism is a mental illness." If we just called it gender identity--which is a more accurate term anyway--this would no longer be an argument.