A woman is a specific kind of female: an adult human female.I do apologize for being obscure. I responded to your "I have precise views about biological realities such as sex, and those views are informed by the science. " The basis of your "precise" views misses the point: "woman" is not simply a biological identity but a social one as well.I am applying you definition of gender bigot to my behaviour. Of course, I know you didn't call me one. Not directly.
The gender cultists wish to change this, so that 'woman' means 'any human who 'identifies' as a woman', and in that case it is a social identity. This might be tolerable, if it did not also come with other demands, such as 'women' competing in girls and women's sports, which were separated by sex for reasons of fairness. It comes with other demands, like 'women' sharing spaces with adult human females, where the spaces were separated by sex for reasons of physical safety and psychological comfort. It comes with other demands, such as 'women' who demand others use a pronoun that conflicts with their obvious and outward sex, on pain of State punishment, livelihood ruination, and social censure, and with total and unrelenting disregard for cultural differences and their painfully indifferent ableism.
If the only demand that gender cultists asked for was the right to say 'I am a woman' (which of course they already have) then I would never think about them again.
EDIT: The above is not an exhaustive list of the demands of the gender cultists. They also believe that there are women brains and men brains, and that the category 'female', not just 'woman', is up for debate (or indeed already means "any human who says they are female").