Hasn't this been done already?
“Second, regarding any crime, male-to-females had a significantly increased risk for crime compared to female controls (aHR 6.6; 95% CI 4.1–10.8) but not compared to males (aHR 0.8; 95% CI 0.5–1.2). This indicates that they retained a male pattern regarding criminality. The same was true regarding violent crime.” [includes sex offending] https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0016885 This suggests biological men are of similar risk to women regardless of gender identity (even following gender-affirmative surgery, which the vast majority do not get), on average as a group. Not more, but not less. Therefore, the same law applies as it's based on the same pattern of offending.
Self-ID makes women's spaces a free-for-all. Currently biological men (a much larger group than transwomen alone) are stopped from entering women's bathrooms by bystanders in the daytime, security guards watching CCTV outside bathrooms in the night time, on the basis of easily discernible sex. The burden of proof is also lower: merely being in the opposite sex bathroom rather than needing proof they were committing an offense, when they were. (This wouldn't apply to the post-op transwomen peaceably using the women's bathroom 'undetected'.)
I think I've come up with some solutions that balance the rights and safety of natal women with those of transwomen, in a way that doesn't invalidate the latter's feelings of gender identity:
Bathrooms: single-stall (floor to ceiling walls), sex and gender-neutral bathrooms
Sports: physical eligibility categories which don’t reference sex, or gender as it’s conflated with; if needed, a larger number of categories
Prisons: Special provisions within so that such people don’t have to deal with gen. pop, whether they are housed in women's or men's prisons. (I'll note that predictably transmen aren't champing at the bit to be included in men's prisons, almost like having a female body is of more material relevance than felt-identity.)
If woman now means adult female human + anyone else who feels they are a woman/would like to be treated as one socially it's a meaningless label, and hampers advocating against sex-based discrimination (that one cannot be opted out of by invoking an internal sense of identity, unfortunately). Does "transwoman" not already imply a certain womanhood born from existing as one socially? Why is that not enough, and instead we have to bend reality and pretend no vast differences exist between the two groups (yes, even after surgeries that alter appearance)? How about equity instead of identical treatment?
Anyway, in the future we'll all be transhuman cyberborg octopuses, and all these tedious discussion of which facilities agendered people ought to use (the one that corresponds to their biological sex, obviously) will be over.