No, they couldn't. Even if it wasn't direct sex discrimination, it would be indirect sex discrimination – unlawful unless it was a proportionate means of achieving a legitimate aim. This is because most people who have a female gender/live as women are also "biologically female" under the EA.
This is quite a complex and nuanced area of law, which I find Maya and her colleagues at Sex Matters tend to oversimplify. Who knows why that could be. Anyway, if the courts hold that this analysis of the Equality Act is not correct – I find it very difficult to see how on earth we are still in compliance with the European Convention on Human Rights. You can read more detail about the challenge and why we think the Code is wrong in law, here:
goodlawproject.org