Other rights, such as the right in the First Amendment to petition the government, might be seen as rules that are corollaries of the type of governmental structure created by the Constitution-a representative democracy-and not as moral rights that exist prior to that structure.
Let me now turn to the second possibility for constitutionalizing rights, namely, incorporating by reference real moral rights. Ronald Dworkin, for example, believes that this is what the authors of the U.S. Constitution were doing when they wrote into the Constitution a right against cruel and unusual punishments, a right to equal protection, a right to the free exercise of religion, and other rights. There are three aspects of such an enterprise worth careful consideration. 
First, if one is going to incorporate real moral rights into a constitution, then one is going to have to subordinate those rights to the various rules setting up the structure of the government and also subordinate them to decisions regarding their content that are supposed to be legally authoritative-that is, decisions that are supposed to settle the question of what the content of those moral rights is for purposes of the legal system.
Let me elaborate briefly on this point about subordinating moral rights. Within morality, moral rights are not subordinate to human institutions and human decisions. Rather, the contrary is the case. Human institutions and decisions are subordinate to moral rights. If moral rights were incorporated into a constitution without making them subordinate to other aspects of the constitutional regime, then they might completely overturn that regime. For there is never any guarantee that a constitutional structure is consistent with moral rights as they really are. After all, the constitutional structure is an artifact produced by human beings possessing fallible moral beliefs. 
Moreover, because the content of real moral rights is controversial, incorporating real moral rights into a constitution would make the content of constitutional law -and thus all law -incapable of being authoritatively determined. For the content of real moral rights cannot be settled by any institution's decision regarding that content, whether it is the decision of the legislature or the decision of the Supreme Court. Therefore, incorporation of real moral rights into a constitution will undermine the settlement function of law unless it is understood that those rights are legally (if not morally) subordinate to some institution's determination of their content. If that were not true, decisions of the legislature and the Supreme Court regarding moral rights would fail to be law in the eyes of those who disagreed with the decisions, because they would see those decisions as inconsistent with real moral rights.
Thus, the first point about incorporating real moral rights is that they must be subordinated to constitutional structures and to authoritative determinations of their content. The second point about incorporation of real moral rights is related: A decision must be made regarding which institution's view of real moral rights should be treated as authoritative for purposes of the legal system. To narrow the focus to the usual suspects, should the legislature's view of real moral rights be authoritative, or should the authoritative view be that of the courts? 
Keep in mind that everyone -the legislature, the courts, and the people themselves-is subject to the requirements imposed by real moral rights. So the question is never whether the legislature is morally free to disregard real moral rights, or whether the courts are morally free to do so. The question is whose view of what those rights require should be the authoritative view within the legal system.