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One rather important subject is the role that the state should play in regards to discrimination. Put roughly, this is a question about the extent of the scope of the state’s power to regulate citizens.
I will be begin with the obvious: the state certainly seems to have an obligation to prevent discrimination in agencies and organizations that are under its direct dominion. This would include the military as well as civilian organizations like NASA and ESA. The basis for this is that a democratic state founded on a principle of equality seems to be obligated to provide equal opportunity to its citizens. To exclude certain citizens on illegitimate grounds would be to rob them of the rights of other citizens in an unjust manner and this would, obviously enough, be wrong.
Moving to a bit less obvious realm, there is the public realm that is not directly part of the state. This would include private schools, private companies, other business entities and so on. On one hand, it could be argued that private entities should be able to exclude whoever they wish. For example, female only gyms should be allowed to legally exclude men (which they, in fact, do). On the other hand, even private entities enjoy the benefits of the state and are under its umbrella, so to speak. As such, if they accept the benefits of the state, then they cannot discriminate against the citizens of the state.
Of course, a private entity could refuse all the goods of the state and this would presumably allow them to discriminate. In short, they would withdraw from the public realm and into the purely private and personal realm. Of course, they would have to refuse everything-road access, police & fire protection, and so on. In fact, they would actually have to leave the state. But then they would be free to do as they wished.
One area where the state seems to have no right to intrude is in the case of purely personal, private relationships. To use an obvious example, a beautiful woman might refuse to date poor or ugly men. She might even refuse to date black men, white men or Jews. While this would be discrimination, this is entirely within the realm of her private, personal life. As such, the state has no business being involved. Of course, buying into this principle would also involve accepting that many existing laws that limit private behavior would need to be repealed.
Of course, the border between the personal and the public can be debated. For example, suppose that the woman mentioned above runs her own escort service. While she can freely refuse to date ugly men, black men, white men, or Jews does she have the right to refuse a client simply because he his ugly, black, white or a Jew? On the face of it, she would be acting in the public realm (in a business context). As such, she would no longer be operating within the realm of the purely private and personal.
However, some folks do argue that businesses should be largely left alone by the state. In a true free market economy, one might argue, the business realm would be a private matter (they do not call it “private sector” for nothing). As such, businesses could elect to refuse to do business with or hire certain people. Those who are fond of a totally free market but who are not so keen on discrimination would probably argue that discriminatory businesses would be sorted out by the invisible hand. After all, they would be denying themselves customers and employees. There is also the matter of the impact of such policies on the reputation of the business.
In light of the above discussion, one key matter that must be settled is the border between the public and the private. After all, the state seems to have far less right to intrude into private matters.