The racial analogue fits because we're another minority group that faces discrimination. Hope that helps.

Seperate but equal, hmm, where have I heard that before?

What do your hypothetical women's emotions have to do with segregation?

Trans women are women but we shouldn't be allowed in women's restrooms because we look different?

Trans women are women but what about lesbians? Because we love different?

Trans women are women but what if a women thinks I might have been a man once and freaks out about it? Because we are different?

Why should these hypothetical women's feelings excuse discriminating against and segregating an entire demographic of women?

I know no woman who has said trans women in the bathroom make her uncomfortable. I've never even seen one.

A lesbians dating preference may be for gold star, should we ban women who have slept with men from lesbian spaces? A lesbian can just choose to not fucking date trans women.

The thought that someone may have been a man once. How horrible. What if she was raped by a woman? Should we ban women from women's spaces to protect survivors?

Do you have evidence for that claim? I promise there are enough factors discouraging participation in women's sports, funding, historical norms, cultural expectations, direct sexism, existing power structures, training opportunities, school opportunities, etc, so forth.

If i sign off as a transgender does it invalidate my feelings as a woman?