Now in America, people associate the phrase “moral relativism” with a group called “the left”. This group is associated with things such as social justice, power struggles/oppression, and diversity/inclusion.
Referring to this group as “moral relativists” is incorrect, and shows little understanding of what moral relativism actually is.
True moral relativists believe there is no inherent, objective criteria for good or bad.
They posit that no system of morals can be superior to any others, since morals are arbitrary, unable to be deduced from the laws of the universe. They believe that things such as genocide, slavery, and war, are not any more “bad” than things like cyberbullying, not picking up after the dog, and stealing from the cookie jar. They believe that good and bad are simply emergent properties of societies, and therefore are subjective and mostly irrelevant.
This is totally different from “the left”. “The left” has a moral system with clear priorities: tolerance and inclusivity, equality, and women's rights. In their context, it is unfair to pay women less than men. It is unfair to descriminate based on race. These things are clearly “wrong” for the left.
A moral relativist would not care nearly as much about these issues, because what is “morally wrong” to “the left”, is simply arbitrary and ephemeral to them.
In the same way as above, terms such as postmodernism and nihilism are also falsely attributed to “the left”. These words have been hijacked so badly that their meaning is no longer clear. I no longer use them myself, and I would avoid using them without clear context.
Despite the above, people should use words however they want to use them. I hate nothing more than proscribed vocabulary, and if the meaning of these words changes over time, so be it. It's just a little annoying if I have to use different words for things that have always been “moral relativism”, “postmodernism”, and “nihilism” to me.