I can understand it, but it's wrong. Because...
You're making stuff up. There never was such data.
This argument has been tried countless times, and it will fail every time. The difference between whites and blacks is not equivalent to the difference between men and women. Absent that equivalency, the argument falls apart.
I'll try again. More clearly this time.
This has absolutely nothing to do with "the difference between whites and blacks" vs "the difference between men and women".
It has, specifically to do with this:
The concept that by granting civil rights to Group A, Group B can claim that - as a direct consequence of that granting of civil rights to Group A - some or all of them in Group B are being disadvantaged (eg by being placed at increased risk to their personal safety).
In the transgender rights situation, it's females claiming that if transwomen are now allowed to use female changing spaces, females will be placed - as a direct consequence of transwomen having been granted that right - in a position of greater risk to their personal safety/privacy/etc.
In the black civil rights situation, it's white people claiming that if black males are now allowed to sit tight up against white females on narrow 2-person bench seats, white females will be placed - as a direct consequence of black people having been granted that right - in a position of greater risk to their personal safety/privacy/etc.
I then went on to point out that, obviously (and correctly) the latter situation had not in any way adversely affected the granting to black people the civil rights they deserved (including the right not to have to give up a whole bench seat on a bus if even one white person alone wanted to sit there).
And lastly, I drew the tacit implied conclusion that the same ought to apply (and will apply) to transgender rights and women's changing spaces.
It was probably my fault for not making myself clear. I realise, however, that there may be some within this debate who - for whatever reason I cannot begin to divine - will continue to claim confusion. And therefore rejection.
That's life, though.