If acts are right or wrong independent of whether or not God disapproves of them, then it is, at least, possible to take a secular approach to moral philosophy. What's right and wrong varies from culture to culture. People's beliefs about what's right and wrong vary from culture to culture. Therefore, what's right and wrong varies from culture to culture. For people often disagree about objective matters.
People disagree about whether the Earth is round or flat.
It doesn't follow, however, that there is no objective truth about the matter. Of course, the fact that the Earth is spherical can be empirically verified whereas it is not clear that moral facts can. But even if moral facts are not empirically verifiable, it doesn't follow that there are no objective moral facts. There is no way to empirically verify that Dan Quayle has thoughts. So there is no way to empirically verify that Dan Quayle has thoughts.