DD I don't want to discuss this with you right now.
However I want you to go away and consider the following:
Have you read what JKR said? You should always read at source information that is controversial to ensure you are not getting a biased version of events.
What part of what JKR said is controversial? You need to be able to quote and to articulate why, not just repeat what others have said is wrong to put a good argument forward.
Why do you think it is acceptable to shout terf at some? Why do you think it is ok to abuse people and call anyone names in a civilised society, even if you disagree with someone? If we all shout and scream at people we disagree with, what do you think would happen?
Do you think calling me names, will help me change my views or further entrench how I feel?
Do you think an argument is a strong one if the only response you have is to resort to personal attacks rather than making the argument on a point by point basis stating your case calmly about why I should change my mind? Do you win hearts and minds by alienating people?
How and why exactly do you think women are discriminated against in the workplace?
Stonewall define homosexuality on the basis of gender not sex. This is regarded as institutionally homophobic by some. Are you ok with women who don't want to have sex with penises being abused and discriminated against? Why is this not misogynistic and homophobic?
Go away and think about these things, and then we will have a civilised adult conversation about it. And maybe you can convince me about where I am going wrong and am bigoted
Until you can, I don't think it appropriate to have conversations about this subject.
Keep being overly reasonable and don't rise to the bait. Keep asking questions and turning everything into a question back at her.
The way to break cult thinking is to get people to think for themselves. So continuely framing things back at people in the form of a question is really effective and makes people question themselves in the process whether they like it or not. Sow the seeds of doubt and work on the cracks and weaknesses of this subject.