Yes I think you can support womens rights i.e. safety (by recognising the differences in strength, endurance, power and aggression), bodily autonomy, equal pay for work of equal value, health care equal to the quality of men and equal opportunity in all areas i.e. sports
You can also support the rights of trans-gendered people i.e. access to good quality health care and research, safety (by recognising the increased risk of violence and mental distress that comes have dysphoria and transitioning), the right not to be descriminated based on your choices i.e. being able to wear appropriate clothes for the gender you identify with and to be treated with the same dignity and respect that you would expect if you were non-trans.
Where it becomes combative is when one groups rights appear to supercede others. This is why todays ruling affects TG women and not TG men. The fact is that most aggression and violence towards women 1) comes from men 2) is exacerbated by the size and power difference between men and women 3) primarily is of a sexual nature 4) happens mainly when a women is alone with men.
This means in situations where 1) a woman may expose her sexual organs or 2) a woman may come into physical contact with a man, or 3) a woman participation in an activity might be judged based on physical power 4) a woman may find themselve alone in private with man which she hasn't got control over require same sex provisions so women can risk assess on how to proceed.
Saying that a TGwoman can access single sex spaces puts the needs of the TG woman (which aren't a human right) over the safety of the woman (which is a human right). Keeping spaces that are there to protect womens safety, single sex doesn't stop any of the TG rights from being fulfilled. We just need to reorientate society slightly to make some space for people who experience being TG and a lot of places are already doing this.
I strongly suspect that the TG people who are just living their lives nothing will change. Maybe they will update identity documents to have TGman/woman rather than M/F but they will already know where they can go and where they need to be careful.