So, what "sex-based rules and responsibilities" is this referring to, exactly?
In the UK, equality legislation and safeguarding laws give men, women and children the right to expect some situations to be single sex.
The right to a same sex doctor for intimate examinations including mammograms.
The right to a same sex domestic abuse practitioner when escaping a violent man.
The right to speak to a same sex police officer when reporting a sexual assault or rape.
The right to only be searched by a same sex officer if incarcerated.
The right to single sex changing rooms, showers, dormitories, hospital wards.
The right to single sex sports, if it is a sex affected activity.
And some of these laws exclude people on the grounds of sex even if they have a GRC.
Stonewall and other pressure groups are trying to change the law and remove these rights, on the grounds of 'acceptance' and 'inclusivity'.
But many of these rules were put in place in response to risk. People were harmed, laws were created to protect others from harm.
If you don't agree with this, then remember you don't get to consent on behalf of other people; then go look up Chesterton's Fence.