Emily's Cat
Rarely prone to hissy-fits
Oh dear.
The analogue is "sexuality is binary and immutable: all people are heterosexual".
This is completely inane.
Sex is binary and immutable. All people are either male or female. Gender identity is completely and utterly irrelevant to the topic.
Sexuality seems largely immutable, but is not binary, and nobody has claimed that it is. The majority of people are heterosexual, which means that they are attracted to people of the opposite sex. Some material portion male people are androphilic rather than gynophilic. Some material portion of female people are gynophilic rather than androphilic. Some slightly smaller portion of people are both androphilic and gynophilic, and this "bisexuality" tends to be more common among females than among males.
Note, however, that such attraction is only couched in terms of androphily and gynophily - there is no third option, because THERE IS NO THIRD SEX.