In terms of racism... I think there is a comparison, though I don't know how well it works.
Imagine if a white person identified as black.
They wore makeup, wigs and prosthetics to look the part somehow; adopted freestyle rap or a Southern "Marmy" accent and new stereotypical style of clothing. OR they didn't do any of that, at all. They just stayed very white and didn't alter anything whatsoever.
I don't think we'd all just say "yes of course, if you feel black then you are".
Many would be insulted that an entire community could be reduced to outdated offensive stereotypes. Or could be turned into just a label which could be adopted or discarded on a whim.
We'd be baffled by kids being encouraged to find their inner-black-self, or being put forward for surgery as a pre-teen if they said they thought they were.
We'd be uncomfortable as they started to qualify for scholarships aimed to increase diversity, and count in crime and equality stats, or the way the medical community approach different group risks.
And then imagine - the first black British Prime minister! Amazing! - while a prominently and visible white man who grew up as one with all the experiences and unconscious benefits therein stands grinning into cameras everywhere.
I actually think there'd be outrage and cries of "racism" from the start.
But with biological sex - another feature we're just born with - people get uncomfortable and confused and want to be kind. They mix gender and sex and sexuality and free expression together, and conflate the trans cause into the LGB battle where people fight to live and love freely without discrimination.
The current push by trans activists does not belong in the LGB category and has in fact already hurt people in it. It reduces women to stereotypes. It damages our rights, and we don't have as many of those as people think. It damages vulnerable people who are in my opinion too young to elect for surgery. The core group of transactivists it benefits are mainly white privileged men.
By all means, we need to protect trans people. Gender dysphoria needs to be treated compassionately; no one should ever be physically or emotionally attacked on any basis. But there should also be limits in society based on innate biological needs too to protect other vulnerable groups.
We should all be shouting "sexism" right now.