> A lack of something is not a property. The legal system lacks infinite number of things. Its not a meaningful definition if infinity is included.

Of course it is! In math, the subset of the reals that includes all non-rational numbers less than or equal to five, has the very clear, very meaningful property of not containing the infinity of numbers greater than five. It also has the very meaningful property of not including the infinity of rationals. Whether you want to define a set by what it includes or what it excludes is merely a matter of convenience, and each can be more or less meaningful depending on context. Infinity poses no problems, because things can be put into meaningful sets.

> It is not OK to treat people different based on gender.

That is your moral viewpoint. There have been many ethical discussions on this. Let me just give a quick outline of why this may be perfectly OK. If the current conditions of the population are the result of negatively discriminating against women, a very reasonable way to correct the social discrimination is by having the law give special treatment to women. There's no point debating this at length here, though, as ethical values are deeply ingrained and are very personal. I just want to point out that there are several ways of looking at this, and several reasonable ethics.

Like I said before, social sciences study the society that we have, not an imaginary model of society made of spherical cows. Similarly, I assume that activists are interested in changing the society we have by enacting laws for this society. Questions of what's fair in an ideal society may serve as inspiration for writing a constitution that should last forever, but simple laws are like a steering wheel. If the car has a flat tire and swerves to the right, a law dictates that the wheel should be held turned to the left, even if it doesn't make any sense to drive an unharmed car in this way and may even spell disaster. If the reality is that the car has a flat tire, then the law should address that reality.

So, when you see a law, don't ask "is it fair in an ideal society?" but try to see what conditions in real society the law is trying to address, and whether or not you think that would help.

> Any such treatment will cause local power disparities, like bias that cause real harm.

I think that's an empirical question. If your goal is to minimize harm (and that is a liberal goal, but not always a conservative goal, so I'm not saying that must be your goal), you just need to see which causes more harm: taking corrective action against existing discrimination or not.

> As a group, victims of crimes is one that should also be discriminated against because of their gender.

Victims of crimes are not a social group. It's a very different form of discrimination.

> Neither is a cultural change away from women being solely valued for their ability to raise children, nor men being valued solely for their ability to support the raising of children.

I think we have a strong disagreement over facts here.

> There exist a long history of nudism philosophy, culture, and values.

That doesn't matter. It doesn't matter how nudists consider themselves; what matters is how they are perceived by society. Society views nudism as a practice, not as an identity (similarly, BTW, to how homosexuality was perceived in classical times, just to show you how things change). In addition, I don't think nudists' power is curtailed by society, which is the main idea here. Whether or not naked bathing is allowed on certain beaches has no effect on the power (influence) of the nudists in society.

> All the effect of discrimination, like being hurt and feeling rejected is current reality of those people.

Like I said in an earlier comment, feelings of hurt and rejection are usually what conservatives attribute to liberal goals because that is a feature of conservative thought. Liberal thought is about power. Similarly, sociologists are not concerned with feelings of rejection -- that's what clinical psychologists do; they study the flow of power. A person like Donal Trump can feel very hurt and rejected, but that doesn't change how much power he's got.

> Two centuries, plus two more centuries, is four centuries.

Yes, but those 400 have barely ended. It's not ancient history. People the age of my parents have lived through that.

> And what material marks has been created for which black people exclusively can have? Is there a reason why the solution to those problems should not be used on society as a whole for anyone with the same material situation? It sound to me like you want solution to only go to people of black people because they deserve it more because of past injustice?

Again, you're talking politics. I don't know or want to talk about what laws are fair. I want to explain how the social sciences analyze society. But just to explain the reasonableness of an ethical system that is different from yours, let me point out that the same material conditions can be due to different causes. John may not have a car because he lost all his money gambling. You don't have a car because I stole it (so now I have two cars). An ethical system that would compel me to give you back your stolen car is not necessarily discriminatory towards John.

> Is it compatible with the successful abolishment of gender segregation in buses that the feminist movement fought for?

Probably. Why? Because social activists like feminists fight for equality of power. The same segregation can be a vehicle for curtailing women's power or it may not. Let me give you an example: Suppose I have a bar and I put a sign on that says, "gays, please sit in the back room where no one can see you". Now suppose I have a sign that says, "gay party every Tuesday night in the back room!" Questions of fairness aside, even though the result is the same, the first curtails a groups power and the second does not. Why? Because seats on a bus or in a bar are not themselves sources of power. I can't influence more people from the front seats of the bus than from the rear seat. What matters is whether you send a signal that some group is worth less. If people see signals that some groups are worth less all day, they come to believe they're worth less, and that is how the group's power is harmed. Now, you could say that the second sign makes people believe that straight people are worth less because they don't get a party. But this is wrong, because it is already an axiom of current society that straight people are not worth less.