I sympathise, OP, my tendancy is towards peacemaking and finding practical solutions to move forward from polarised debate. It takes courage to reject the relative safety of either entrenched group and to stand in what Brené Brown calls the wilderness, and to get to the heart of the matter and form your own opinion rather than just picking a side. I think it's a good instinct to have.
When faced with a hugely polarised issue such as this, I get really curious about why people think or act differently from how I do and that helps me to understand where they are coming from, even if I still disagree.
Initially, though the concept of gender identity seemed to rely on sexist stereotypes and conflicted with my feminist beliefs, I too thought the rhetoric from some GC feminists was insensitive and unkind. I feel compassion for those suffering from body dysphoria and I thought the directness of referring to people by their unwanted sex characteristics was uncharitable and unnecessary. I wanted to be respectful of gender non-conforming people living their best lives, whilst critiquing the logic of adopting their dysphoric thinking as biological, legal fact given some of the (I thought) unintended consequences for women.
In the end, as I have learned more, and seen more consequences and outlandish demands and boundary pushing and downright hypocrisy the utter disregard for females, for how we wish to identify or organise ourselves - I have understood better why GC feminists are so focused on honesty and clarity and will refer to male bodies and attributes.
One of the main reasons for this is that language affects perception so much particularly combined with short circuiting logic like "TWAW". Something that can sound harmlessly inclusive of Transpeople in the disembodied online space, but completely impractical when dealing with physical sexed bodies in prisons, medicines or sports.
If you'd like to learn more I would highly recommend the book, Material Girls , or even better her audiobook read by the author. She is very compassionate towards trans people and dives into gender ideology and the consequences of this legal and social fiction.
Another book I would highly recommend for you, not directly about the conflict between women's rights and gender ideology but about the many ways in which women have been disadvantaged by our differing physiology not being accounted for in many areas of life and why all of this matters is Invisible Women . I thought I knew what feminism was needed for before that book but I had no idea really of how pervasive man as default human has been into all areas of human knowledge, technology work and life and the consequences of that for women today.
Growing long hair and a putting on a dress doesn't scratch the surface of what it means to be a woman. How could it possibly?