“Relative Moralism”; a concept shunned by most organized religions. Essentially, it recognizes that societies are built upon commonly agreed-to “Game Rules” (the larger and more sweeping of these usually codified into Law), but these Rules are often contradictory amongst themselves, and sometimes even contradicts the mammalian primate behaviors of humans. More tension and conflict arises when two cultures meet, due to the fact that many of these Game Rules (especially those that are not Laws) are unspoken, ingrained, and highly conditioned.
In addition, Tribal Culture dictates actions that define it as different from the rest of Humanity, most often through essentially meaningless habits and symbols. Because these actions are habitual, most people cannot recognize that the majority of their behavior makes absolutely no sense to someone from outside their culture.
Relative Moralism attempts to reconcile different Cultures by establishing larger Game Rules that everyone can agree upon, and leaving the rest alone. However, most people are unable to avoid their own habits, so the system, while mostly effective, becomes flawed when language breaks down, and compromises cannot be reached.
So, people can indeed have separate sets of morals, like the Jew that eats pork, or the Catholic who doesn’t think the Pope speaks for God. This does indeed imply that there is no “ultimate” right and wrong: Even something as big as “don’t kill people” breaks down in the likes of war, death penalty, abortion, self-defense, etc. Most organized religions don’t like this, because they are partially founded on the belief that they have “the” answer to “everything”.
As far as determining overall what is right and wrong, you could go for “do unto others as you would have them do unto you,” or “Love, and do as you will,” or even go so far as to say “if it doesn’t harm anyone, it is permissible.” Of course, a person can find outlandish examples in the extreme regions of this (my favorite is, why not eat the dead? It’s certainly not harming anyone), but so far, it’s the best we can do in a so-called “free society”.