Richard wrote:..should they always be allowed to demand to do the same jobs that men have?
Generally speaking probably yes.
But perhaps not in certain cases.
I think the answer to that is yes, they should be able to demand "access" to the same jobs, so long as they can demonstrate they have the appropriate levels of skills, ability and aptitude for the job in question.
To pass an interview for such a job they would have an equal opportunity to demonstrate they are a suitable candidate in the same way as any other applicants (male or non-binary...) and be weighed against these criteria with complete independence of their gender.
The interview process is where so much of this falls apart as there are still a majority of men in the recruiting capacity and there is a completely natural bias towards more of what has worked well in the past - ie more men.
For equality to work the recuiters need to be very concious that they must treat all applicants the same - having one female in a team of males may result in issues further down the line but we cannot let the possibilities of discrimination later impact the opportunity for the candidate to do the role.
Not long before covid, I had several management training courses that covered equaility (in all aspects) in the recruitment and ongoing management process. It was very informative and showed so many areas where we bring bias into the recruitment decisions subconciously that the HR team are scrubbing all references to gender and race from CVs before giving them to us for shortlisting candidates and are sitting in on further interviews to run through scoring candidates fairly and equally to find the best bet, puting rest to going on "gut feel" for a hire.
Having said that, my last 2 hires were put out to the open market and I was then given an explicit instruction verbally from the head of HR to hire a woman as the team had too many males to meet their balance objectives for representation. I did point out the hipocracy of the instruction but was told to get on with it.
I guess it is only reasonable that the playing field needs to be tipped in favour of the victims of discrimination for a while to get us back to a more sensible balance.
Sorry, I've rambled on a bit, I hope some of that explains how I've seen it handled in real world recruitment at the moment (my employer is a very progressive one that I have no complaints about).