No, not necessarily losing.
I am saying that cis-women likely won't win in some sports if they compete with trans-women. Those sports where a genetic advantage might be conferred by virtue of being born male.
The right to compete and be included within a structure designed for all women is what trans-women are after. The right to compete in a FAIR competition with other women who do not have an unassailable advantage over them is what matters to cis-women athletes. Those are difficult issues.
Any woman who isn't an athlete isn't marginalised because they are part of a group of people who could compete if they wanted to but who have no fair advantage.
As an example of what I mean. Had Caitlyn Jenner competed as a trans-athlete then her performance in 1976 as a decathlete would've...
1. beaten the women's world 100m sprint at the time. (10.94) vs the record at the time (11.04)
2. shaved 2 seconds off the 400m world record from 49.75 to 47.51
3. Added 7cm to the High Jump world record.
4. Added around 30cm to the Long jump world record
5. Added 3m to the world record for javelin throwing
Now, before we go any further.... let's remember that Caitlyn Jenner wasn't a specialist in any of these... she was a decathlete. A jill of all trades. Was she behind other women in some of the decathlete sports. Sure... but I think there's a reasonable argument to suggest (as Caitlyn herself does) that it isn't fair for trans-women to compete with cis-women on the sports field in SOME sports (though not all).
And given she could run the 400m in 47.51 seconds, it's worth noting - she'd still be the women's world record holder 46 years later. No woman has run the 400m faster than Caitlyn Jenner did in 1976. Does that seem fair to you?