You seem to not understanding the current situation.
To say "we have never checked genitals before" is to not deal with the political reality of the aggressive attack by TRAs on women's sex based rights.
We never checked before because we didn't need to. Because most people lived and understood the reality of sex.
And I suspect that in the past the odd transexual who had gone through surgery, even if the didn't "pass" probably wouldn't have been challenged.
But thanks to the queer inspired attack on the norm, we now have a situation that is nothing to do with gender dysphoria but to do with at one end people whose lifestyle is all about identities and nothing to do with dysphoria let alone surgery, and aggressive men who whether they still have a penis are about pushing the boundaries of women having the right to demand their rights.
So if you are thinking women are being a bit over the top, it is only in response to the overt attempt to undermine women's sex based rights.
So what the Lib Dems are doing in their virtue signalling is, almost worse than claiming they would change the EA, is to perpetuate the damaging lies that you can change sex.
Gender re-assignment is already covered by the EA.
But attempts to say the word sex in the EA is open to re-interpretation is an attack on women's rights. And it shows that when sex was firts included in the EA nobody thought the law had to confirm that sex is biological which shows just how far, across society, the TRAs have undermined the word.
And as the Judge said, sex in the EA is the only one that is discriminated against within the law if it is said the TW are the same as actual women.
(Just to add as often said on other threads, the EA does not cover those who "identify". GR only refers to those who have undergone re-assignment surgery or are on the pathway. So if the law was changed it would only cover the approximately 10,000 with a GRC ie the "legal women" and not the trendy identities which is who this vote is aimed at. )