However, transwomen do not make the situation worse and they are certainly not at an advantage compared with men.
I'd say adding men, particularly late transitioning men that have benefitted from male privilege for decades, to a group that is permitted to benefit from hard fought for and sex-based rights intended for women, absolutely dilutes those rights and makes the situation worse.
Women that have fought for, eg, all women short lists, to address the imbalance based on sex on certain positions of power. A transwoman being placed on that list is benefitting from something put in place to benefit females and address the sex based discrimination they face. Likewise, single sex refuges fought for on the basis that women wanted to be safe from the male sex due to abuse. Diluted by suddenly allowing penises in.
Conflation of gender and sex in reporting - key issue in establishing trends that can be addressed preemptively.
We saw with Rachel Dolezal that no matter how much a white woman feels or believes themselves to be black, that isn't enough to class herself as black and take advantage of things put in place to address the societal imbalance of racism. But somehow it is when it's sexism that's involved? It's just cultural appropriation.
The discrimination transwomen face as compared to men is based on the fact they're trans, not the fact they're women. It's unacceptable but nothing to do with discrimination based on the sexual capability of their sex. Women isn't a category for 'not-manly-men' so, frankly, in terms of categorising what a woman is, it's irrelevant whether trans people are discriminated against in comparison to men. The discrimination they face is different and needs to be addressed differently.