Why would morality have to progress? Is stealing going to become ok? How about murder? The principles of the individual freedom, private property, freedom of thought are timeless things. Those who wish to tell us what to eat, what we can drive, where we can live, what we must think and what we have to pay for, are immoral, not advancing in their morality.
Cultural relativism defines progress as replacing the old ways with new and improved ways, but moral progress doesn't necessarily mean that the ways are improved. It is not very clear if a changing society is getting better or worse.