The idea that male-female gender is an arbitrary social construct is postmodern nonsense.
There is pressure now for some health workers to tell women that they do not have breast cancer. They have “chest cancer.” And this is not to mention the new pressure to call everyone “they,” even straight men and women.
Though estimates vary slightly, about 90 percent of the population in most studies identify as traditional male or female. The now-popular denial of gender differences means denying the self-evident.
Here is a simple way to refute the postmodernists. Take off your clothes next to someone who was “assigned” a different gender at birth (i.e., male or female). Look together into the mirror. Do you see a difference?
If that will not do, irrefutable evidence can be found in DNA. Women are capable of bearing children. Men are not. Women are capable of producing breast milk. Men are not. Women can develop ovarian cancer. Men do not have ovaries but can develop testicular cancer, a disease for which women will never need to visit the doctor. Women have more female hormones than men. Men have more testosterone. On the average, men are bigger, stronger, and faster than women.
These physical differences are why men and women have different sports leagues. Furthermore, more people prefer watching certain male sports than female sports because men, on average, are better athletes. In the most recent World Cup of soccer, 3.5 billion people watched the men, and about 700 million people watched the women. It is fair, then, that male athletes are paid more. Why shouldn’t they get paid more on the average when more people want to watch them? (Of course, female athletes should try to get the best deals they can.)
This does not apply to mental work since men and women are, on the average, equally intelligent, so level of job skill should rule salary.  
Now, what about other sexual/gender categories? The most obvious are gays. But now there are additional categories, such as non-binary, intersex, trans masculine, trans feminine, gender queer, and agender. These people should not be shamed, treated as sinful, or given less-than-equal rights.
Claiming that gay and trans people are sinful is both untrue and unjust. Most often, those who embrace this immoral view use the Bible (or other religious writings) to support their hateful position. Yet, the Bible is not an authority on biology. Genetics clearly play a role, probably a substantial one, in a person’s sexual orientation and gender identity. Condemning someone for something out of their control, such as their genes, is irrational, equivalent to condemning someone for their height or hair color. More importantly, gay and trans people should never be considered sinful, even if genes were not a factor. People have the right to make choices. If you do not care for people of a certain sexual orientation or gender identity, just leave them alone and spend your time connecting positively with the people you do like being with. Every adult has the moral right to connect voluntarily with others of their choice. Law abiding people who have a different orientation or identity than you will do you no harm, with one exception: marrying or partnering romantically with someone while faking one’s sexual orientation or gender identity is a serious, moral betrayal. People have a right to know what they are getting.
That said, athletic organizations need to address issues of fairness related to women with high levels of testosterone and more muscle mass competing against, and routinely beating, cisgender women in sports competition. Some organizations and state governments are looking at ways for intersex athletes to form their own sports leagues and compete against each other. I agree that this is a fair solution.
Beyond physical attributes, there are differences in gender related to mental health and personality (Murray, 2020). Contrary to some viewpoints, these differences are not simply arbitrary stereotypes. Consistent, average differences exist between men and women. Men are more likely to have autism spectrum disorder, conduct disorder, attention deficit disorder, schizophrenia, dyslexia, stutters, Tourette syndrome, and possibly alcoholism. Women are more likely to suffer from major depression, bipolar disorder, generalized anxiety, panic disorder, obsessive-compulsive disorder, post-traumatic stress syndrome, and anorexia nervosa. However, these are only averages so it should not be assumed that every group member is the same.
Now consider personality traits (also from Murray). Data have been gathered across decades and in 25 countries, and the average differences are quite consistent. Some studies measured as many as fifteen factors, others only five. But a strong, overall pattern emerges: women are, on the average, warmer and more sensitive toward others and more open to emotions than men. These average differences appear even in infancy. The measured personality differences are even larger in the more advanced countries.
Of course, belonging to a group that is generally stronger at athletics or more open to emotions does not make any one individual morally superior or inferior, nor does it mean that there is no variation within genders. There obviously is.
 Men and women do not differ in overall intelligence. By using objective measures of assessing intelligence, we know that men and women are on the average equal. In both cases, the IQ distributions fit the same (normal) curve.
 Leadership is primarily intellectual. Leading requires a clear vision and an effective plan for actualizing the vision. In short, leaders have to know what they are doing, making leadership an intelligence-dependent role and not a testosterone-dominant role. Both men and women can do it. They might have different styles, but style is not substance (Locke, 2022). That said, one exception might be necessary: roles involving military combat. The military exists to fight and, logically, is much more heavily populated by men than women. A very small number of females may succeed in combat roles, but most are best suited for non-combat-related leadership roles. In the police force, issues of gender are usually unrelated to leadership as policing involves many activities besides physical combat.