For me this is a big flaw in the argument. If you succeed in banning trans women from female spaces then trans men will be included in female spaces and I don't see how that accommodates vulnerable women.
Not with a third space provision. Third spaces might also solve the non-binary question, I think.
Allowing self-identified trans men into male spaces should be with the consent of men. It is true that testosterone can help the trans man "pass" much easier, but men should also be consulted.
The power dynamics and risks are also important to contextualize. The extra risks of allowing any and all self identified transmen into male spaces are being knowingly taken on by the trans man himself. He is the one who is most at risk, and he therefore can give informed consent. As he is biologically female, he is not likely to pose a significant risk to biological males, but again, men should also have a say for reasons of privacy, comfort, etc.
The extra risk of allowing any and all self identified transwomen into female spaces is not actually being carried by the transwoman herself. Because males are statistically more likely to be sexual offenders or violent then actually the harm from such policies will be borne by the females who are already in that space. Women right now are not even being properly consulted as to whether they think the extra risk is worth it.
So in other words, transwomen are not knowingly taking on an extra liability as a fully informed individual in order to go into women's spaces. What's actually happening is that in order to accommodate transwomen, females as a group have been demanded to remove their boundaries, without informed consent or even a seat at the negotiating table, and with potentially very significant costs to women's comfort and safety.
The reason transwomen in women's spaces is the big issue, is because the people taking on the additional risk are the already vulnerable natal women, and therefore it is their opinion that really matters.