I think there are a few things tied up in this.
In general, I think real discrimination on the basis of sex should be minimised. I think a lot of things, like work, should be open to everyone who qualifies. I usually don't care whether there are some jobs that are male or female dominated, because I don't think it makes sense to pretend that male and female lives are or should be identical. If that causes problems - like fewer women have pensions - then find ways to make that situation better.
I do think politics should strive for something closer to equal numbers of men and women, and that can be carefully supported through intervention.
I do think privacy or modesty is a valid reason for separating the sexes. I don't think it's really discrimination though, or that is the best way to think about it in the law. To me modesty , which is of course an old fashioned word, is about respect for the body in terms of the whole person. I think we need a way of recognising that yes, there is a cultural component to how we practise that, but that is ok, it doesn't make it less important.
As far as things like medical care, I do think there is probably always going to have to be some compromises. Where I live for example, a man needing nursing care will be very luck to get a male nurse. And we have a GP shortage, and while technically you don't have to take the first person available, the fact is options may be limited. Most GPs are women, but they also work fewer hours, so you probably have an even chance of getting a man or woman. But I think that in the context of professional care maintaining modesty is possible even in those circumstances.
One thing I have really come to dislike is that we have a lot of special clubs and camps and such for girls only, and not for boys. I think it's ok for men and women to have separate social clubs if they want, and I think it's very good for young people to have these, where there is good leadership. They don't exist for boys here at all, even scouting is mixed. So in principle I like the idea, but not the actual focus. I think the problem is that people think about this as only trying to improve things for women, and not in terms of the idea that boys and girls may benefit from some separate mentoring and socialising, even if there was no sexism to combat.