I think the UK trans debate has teased out the sticking points for feminists, and it might be useful to lay them out given that the battle in the US, with a very different legislative environment, is just starting.
The GRA of 2004 gave trans people the ability to change legal sex via a GRC, but only if they had a psychiatric diagnosis of dysphoria and only after having lived in role for 2 years. The spousal veto gave spouses a chance to annul or obtain a favourable divorce.
While this ultimately created the loophole in women's rights that we've been fighting against in the last few years, it catered for a tiny number of dysphoric transsexuals and so did not have an enormous impact.
Discussions with trans friends and allies make it clear that, although surgery wasn't a requirement for a GRC, the diagnostic procedures were expected to trap and exclude males who did not want surgery, thereby preventing fetishists and opportunists from exploiting a GRC.
The Equality Act of 2010 defined the various protected characteristics, including both sex and 'gender reassignment', and provided for sex-based exemptions, under the auspices of which it is legal to exclude trans people from some single-sex spaces and services.