IF women are payed less than men for the same work AND gender is a social construct and can be chosen, THEN it follows that those who currently identify as women voluntarily accept lower wages.
Therefore, assuming the pay gap exists, it exists only due to free decisions. The persons identifying as women accept lower wages because it is more important to them to identify as women than to get a higher wage. The persons identifying as men do so because they value money more than the opportunity to identify as women.
BTW, 80% of the refugees currently streaming into Germany chose to identify as men. The reasons are as of now unclear.