Most of us on here believe in using normal English - not least because it's confusing to many vulnerable groups not to, some because it's all WE can cope with. It is a huge cognitive load to use wrong sex pronouns. It also has safeguarding implications. I will not model to children that they need to lie about the evidence of their senses to placate the feelings of others.
The OP, like me and 99.9% of the population uses sex based pronouns.
You have no clue about parenting if you think giving in to demands from a child that police your actions and speech as an adult is in their best interests. If the child wants to use different pronouns in her speech the OP has said that is fine, however she does not get to dictate what her mother says and does. If she did, it would be very destabilising, children need boundaries (particularly in the teenage years) if they feel they do not have any, even if it's what they say they want, it never ends well in my experience and I work with young people. The parents that give in over and over again, ever time the child pushes, are the ones that have the difficult time. The parents with stronger boundaries have children who do better - children appreciate the consistency and constancy.
Third person pronouns are generally not used when speaking directly to a person so it really shouldn't matter much.
What you are suggesting goes against what the Cass Review says. Why do you think you know better than a highly expert paediatrician? Do you have medical expertise? Social transition is not a neutral act.
Yes, saying 'no' to your child hurts their feelings in the short term. It starts in toddlerhood when they demand you let them eat off the floor like a dog, or that you only feed them ice-cream or that they go outside naked in the winter or let them play in the road. They have screaming meltdowns about how you're ruining their lives and they genuinely feel this and believe it. However, parents on here truly love their children, are the adults primarily responsible for their safeguarding, and know from years of experience that sometimes to ensure the wellbeing of their children they have to accept their children won't like them at times. It's about safeguarding and supporting them, not being liked.