I respect the advice to ignore it but I am alas a person who can't allow the politics of hate to go unchallenged...
Online hate and hate in person are two different things. I will post below my advice if you do want to challenge the hate online, in person it depends on how confident you are in yourself.
It is often easy to just ignore it but don't take it to heart whatever you do. This woman is lacking facts and is easy to disprove.
If you do have the confidence to face her, then don't get angry, and show love in the face of hate. You can go one of three ways... 1) I would simply say, 'how dare you! I am a woman and I bleed!' After all how does she know you are not CIS? There are plenty of cis born women who are more ugly that we are even when we are presenting male.
2) Say, 'I've done nothing to harm you, why do you feel the need to hate me?' And I would just repeat that until she gives you an answer. Then reply, 'do you not feel that to be human you must show humanity?' Claim the moral high ground.
3) Go over the top with the love. Blow her a kiss and say, 'I love you too hun' and either walk away or follow it up with, 'now give me a hug and it will all feel better' and then open your arms to her.
The best way to tackle hate is with love.
Now for the online stuff... this is the advice I gave not so long ago on Transgender Zone...
I understand where TERFs come from in their arguments. They just feel that we are men invading their space and that we are using our 'male' privilege to take control of the feminine. We're not content with ruling the world but want to invade and take away what they feel is their birthright. By refusing to accept us as female, they see us an easy target to attack and transfer their pain and their hatred of men. Some may be women who have been genuinely hurt by us, such as wives, girlfriends, and even mothers. They find then lash out at us all because it is easier to hate than show love and understanding when you feel pain. Most, however, are simply man haters who refuse to accept that we are not men because of how we were placed at birth. Their arguments tend to focus on biology and are very weak and easy to disprove. The secret is to not allow them to put you on the defensive but instead attack their arguments with examples and facts that disprove what they are saying. We don't need to argue our right to exist, we merely have to disprove their argument why we shouldn't exist. I don't think ignoring them helps our cause but unless you know how to argue against them (and the alt-right/bible bashers), you probably do more harm by engaging them than good. Always seek the moral high ground and never let them anger you. Always finish by asking them why they hate you or why they seek to oppress you. Remember that your argument is not simply with them, and it is unlikely you will ever change their mind, your argument is to convince the people reading that the op is a bad person and you are reasonable, calm, knowledgeable, and loving. Don't hate the hate but spread love instead. Keep the moral high ground.
And with regards to the LGBQ+ community who hate us...
It is amazing how quickly the oppressed become the oppressors. Something more productive would be, 'How about instead of attacking us about our condition being a mental health issue (worthy of electric shock treatment to cure us?), we instead focus our energy in tackling the prejudice that we ALL face before we find ourselves behind barbed wire with pink triangles and a smell of gas. Our enemies laugh at us when we are fighting among ourselves, using their arguments, and doing their job for them. We are not your enemy but your friends and allies. You need not like us or help us, but please don't hate us.' Keeping the moral high ground, making them question their hate, offering the hand of friendship and love, and not losing my temper. I hope that helps?
