In an ideal world, people would agree to defend a specific list of rights. That way, individual conceptions of what constitutes "rights" would not conflict with one another, and the charge of discrimination would be impossible to make. Of course, it isn't an ideal world, and in practice, functional governments must practice some discrimination in some form.
Governments do not and indeed cannot outlaw personal discrimination in a world where people disagree on what constitutes a "right." But governments can and do choose which actions to discriminate against. Certain groups of like-minded individuals will always have the applications of their views limited by government.
Some forms of government discrimination are obvious and necessary. Obviously, governments discriminate against those whose belief systems encourage evils such as ritual murder, by not allowing those individuals to put their practices into action. Belief systems promoting actions harmful to life, liberty, and property are discriminated against by government.
There are other belief systems that are not directly harmful to life, liberty, and property that also face widely accepted government discrimination. Racism is a perfect example of a belief system that is (rightfully) discriminated against. Before the Civil Rights Era, a web of laws discriminated against people of color. Now, the shoe is on the other foot - businesses cannot, by law, discriminate against people because of their race.
Racist business owners could validly complain that they are being "discriminated against" by government. Their freedom to act in a manner which unfairly judges others based on the color of their skin would indeed be limited by law. And 95% or more of the US population would rightfully ignore their complaints, viewing discrimination based on race as detrimental to society.
Questions of discrimination are still being resolved in other areas. The members of the same-sex marriage movement are rapidly coming into conflict with defenders of religious liberty; the supposed "freedom to marry" is clashing with religious freedom.
These two freedoms cannot coexist peacefully. Society will be therefore forced to choose between upholding the old freedom of religious liberty, as outlined in the First Amendment, and the new "freedom to marry." And in making this choice, society must necessarily practice discrimination against one of these two groups. Either individuals in homosexual relationships will not have the freedom to marry, or the members of religious institutions will be forced to facilitate actions they oppose on religious grounds.
When government is forced to choose between two conflicting conceptions of rights, the defenders of at least one of these conceptions of rights will complain of discrimination.
