And we're not even talking about a context where biology matters. You just wanted to vice signal.
If you want to make this an SBGG criticism, I'd love to see you even get close to proving abuse beyond singular instances. Even all the right-wingers that said they'd change their gender marker to make a point did not. Because people don't do that lightly.
EDIT: I'm rate-limited on comments, so if you come back here and read this, thank you for sharing from experience.
You will still have to deal with a ton of bureaucratic overhead and little moments where this is disclosed. For instance, your health insurance (and doctors) will usually know (the marker, not that you're trans, i get endometrial cancer screening recommended to me) and start to bicker about non-standard healthcare (i.e. I can get my estradiol tested at my GP, but for testosterone I need to see an endocrinologist) and your social security / employer will know (I also have at least 3 aliased social security numbers at this point).
Pure gender marker changes absent a name change are a lot less common, so it's not exactly well known territory.