Our obligations to each other originate in common goals. If a community wants to run a soup kitchen, the members are obligated to bring soup (or other food), staff the soup kitchen, etc. If a business wants to make a profit, the CEO, managers, and employees all have specific tasks that they are obligated to perform so that profit is made. If they fail in their obligations, the business fails.
In the same way, insofar as a society has common goals, the members of the society have obligations to each other to bring about the common goals. These obligations imply certain rights; every member has a right to demand that the obligations be met and a right to see that the goal is achieved. If the goal is contingent or not absolute (such as the amount of profit or the size of the soup kitchen), then the rights are also contingent or absolute. In fact, profit-making and establishing a soup kitchen are both themselves contingent goals, contingent on some higher and more absolute goal: a happy and just society. True, either one can be used wickedly, but in each case, the ultimate goal is something else entirely.
The more absolute the goal, the more absolute the obligations (and thus rights), but also the general or abstract. The Bill of Rights gives Americans the right to bear arms for the goal of a well-ordered militia. That is a specific right for a specific goal, but the militia itself is to be formed for a more general and absolute goal: the safety and protection of the community. However, a militia of freely-armed citizens isn’t the only way to protect a society (though it may be the most just). Thus, the right to bear arms for this purpose is not an absolute right. If it was thought that only arming the best-trained citizens was the most just way of protecting the community, then only the best-trained citizens would have a right to bear arms, according to the common goal of the people.
However, people do not just have the right to the means to the goal, but to the goal itself. In the previous example, the goal is a safe society. Because this is a common goal that applies to everyone, it is a right that everyone has (and equally). How that goal is achieved, through what means, is dependent on what means are available, and of course the effectiveness of the means. Rights (and obligations) are distributed according to the means of the members of society so that those who have greater means have greater obligation (and a right to fulfill that obligation!) Ultimately, though, all of these rights and obligation are in service to a common goal. Rights are as universal as the goals to which they are applied.
The question, I suppose, is, “Are there any universal goals that apply to every human being.” If there are, then we have a foundation for a sense of “equal” or “universal” rights (and the obligation to fulfill these rights). Two goals that come to mind that apply to every human being are a happy and just society and union with God. There may be others.
If we think about these two goals, it is clear that one is more universal than the other. Union with God (according to some definitions, the ultimate being, according to others, being itself) is the ultimate universal goal to which all other goals are subordinated. Everyone, therefore, has a right to pursue this union (and in fact, some say, a duty.) We also have an obligation therefore to ensure that people are able to pursue this union. This ultimate universal goal implies ultimate universal rights and obligations, though the means to achieve the goal may mean that the rights and obligations are not identical for every single person.
However, even if we were to deny the existence of God (a dangerous prospect, to say the least), a happy and just society is universal enough, since it does indeed apply to all people (if you would like more information on this goal, consult your Aristotle.)
If the goal of a happy and just society is universal, then the right to that goal is universal, as are any rights that are necessary to achieve that goal. Of course, the definition of “happy” and “just” are operative. What is justice? What is happiness? If any society is to have this goal, they must first determine what it means. Perhaps we shall discuss these questions further at a later date.
In my previous discussion of equality, it became clear that on a purely material level, we are not equal in means; neither do we have equal rights in our contingent, material goals. However, on a spiritual or supernatural level, one that demands justice and a union with God, the rights to pursue these things is universal, though not all ways of pursing them are effective or good. Our universal rights do not mean that we have a right to do whatever we want, but rather that everyone has the same right to practice good means to a universal end, whatever those means are and whatever that end is.