The answer to this question, to my mind, is two-fold. This is not to say that there are two different answers, but that the one best answer is to be seen as having two angles of view within it.
In an absolute sense, all morality is made up and is subject to change, subject to interpretation, and therefore can be seen as relative to the individual.
However, morality is generated with a purpose, it seems: to make community life possible (and harmonious). The existence of morality is attributable to social living. We have shared rules of conduct, a shared sense of right and wrong, and these shared rules allow us to live together, to set limits on the rights of individual freedoms in light of what is best for (1) the group and (2) other individuals within the group.
This means that individuals cannot truly or practically create a singular moral code. In fact, the attempt to do so is construed as something close to a pathology and has been explored in literature in characters like Captain Ahab, Colonel Kurtz and King Lear.
The absence of an absolute basis for right and wrong does not imply that right and wrong becomes an issue of individual choice. With this being said, however, we can also easily point to the role of individuals in changing specific moral and ethical rules.
Ultimately, this is a matter of opinion -- there is no way to prove this and only you can decide for yourself what you think.
In my opinion, there are things that are simply morally wrong. These include violations of other people's life, liberty and property. In other words, I believe that killing other people (except in a very few circumstances such as self-defense and war) is morally wrong everywhere. So are things like enslaving people (taking their liberty) and stealing from people (taking their property).
However, I realize that there are things that are relative. For example, what constitutes taking someone's liberty? Is a woman's liberty taken from her if her husband controls all the property (by law) once they are married? I think so, but I can also see where you might argue that that is relative.
So, overall I believe that basic human rights exist. However, I also believe that it is not easy to know where basic human rights end and matters of personal or cultural opinion begin.