The problem of gender pay gap is a really hard one to tackle. You have to be a fool to pretend there is no issue, but the number of causes is incredible at the gender, education, industry, company and individual levels. Every time there is a public debate around that topic you end up with two major groups, one saying that women work less or are less productive because of XYZ, the other saying something close to "it's…
Since gender only seems to play a very minor role in wage differences between men and women, as opposed to say, willingness to work full-time/overtime, personality, and job choice, it is not at all clear that the 'gender' pay gap is a problem that needs tackling. I believe systems that strive for equality of outcome and put group identity above individual qualities will only create more injustices, not fewer. If the…
But isn't personality heavily influenced by gender, job choice by education and stereotypes, will to do over time by lifestyle (getting the kids from school, ...)
I agree with your point of view on identity politics, but you seem to assume that the current "system"* is neutral and isn't favoriting any demographics right now. Last time I checked, studies tend to show that the "gender pay gap" isn't entirely based on gender, as you said, but still, a non negligible part of it is.
* I don't like that word but can't find better