I'm 100%:supportive of everyone's right to live and dress as they please, wear makeup and hairstyles as they choose, and use the name they want. That harms no one.
No one should be discriminated against in employment, provision of services including housing, medical care etc. No one should be abused ever for being who they are.
But it fundamentally does harm women and girls if a man who chooses to wear a skirt, makeup and long hair is described as "living as a woman" and it is also harmful to describe a woman who chooses trousers, short hair and no makeup as "living as a man". This is harmful because it places unreasonable expectations of performance of femininity as the defining feature of womanhood.
Women and girls are discriminated against due to their sex not their gender. Transmen are discriminated against due to both their female sex and due to their transgender status so my intersectional feminism is very much concerned for them. Transwomen are not discriminated against because of their sex as they are male. They are discriminated against because of their transgender status and they should not be - but that isn't the fight that feminism is concerned with. Feminists centre women.
When examining the rights of a transwoman the appropriate question is not whether they are being treated the same way as a woman would be, but are they being treated the same way as a gender-conforming male would be. If they are being denied housing, employment and services that would be available to a gender-conforming male due to their trans status then that is discrimination. Refusing to address someone by their chosen name is unreasonable. But a male not being allowed access to spaces, services and opportunities reserved for females is not discrimination.
There is no need to describe a transwoman as a man though obviously. Transwomen are transwomen - they are male at a biological level but wish to opt out of the gender expectations of masculinity. That's fine - fully supportive. There is nothing at all wrong with being a transwoman. Transwomen are not women though. Why pretend otherwise? Why be ashamed of the trans prefix? There is no harm or shame in being trans so own that prefix as a badge of honour.