There are two interrelated rationals that sit behind the argument that the biological birth sex of trans people shouldn't matter. They are rarely fully articulated, because they have obvious faults and are mutually contradictory (in spite of their interrelation), but you will frequently find them invoked obliquely.
1 . Sex in the modern age is irrelevant. We now exist in a post-sex world and sex is no more than a choice and social custom akin to selecting Mr, Ms., Mrs., or Miss. The choice of which sexed service or space to use is simply a function of personal preference and the correlation to biological sex is a dead anachronism, like the idea that needlepoint is some how only for females.
Under this rational:
Why create that division at all?
Because 'sex' is a a self selecting association, like a hiking club. Excluding someone from that space or service because of their biological sex is simply hatred against trans people - everyone else gets to use the service of their choice only trans people are excluded.
If the difference between men and women isn't our bodies, why is it such a huge problem for TRAs to admit that humans nevertheless do have two sexes with different bodies?
Differences between sexes should simply be seen as differences in certain attributes among the human population.
2 . Sex in the modern age is still relevant, but trans people change their effective sex. By getting surgeries and taking cross sex hormones, trans people do in fact change their 'biological' sex. It should be assumed that most trans people are totally undetectable and that it's only a few outliers who can be clocked and a very few people who aren't even trans who abuse the trans category. In the same way that were don't discriminate against a class even those some people in that class abuse it and others pretend to be in the class even though they are, trans people shouldn't be discriminated against (excluded from single sex services and spaces) due to a few bad apples.
Under this rational:
Why create that division at all/why is it such a huge problem for TRAs to admit that humans nevertheless do have two sexes with different bodies?
In this scenario, the division should be maintained. Trans women are not safe in men's spaces and their dignity is violated by being forced to use them.
What's notable is that in TRA arguments they will switch back and forth between justifications, e.g. no one cares what sex toilet you used, it's just a place to piss, but, and also TW are unsafe in the men's toilet.