Modern morality is often termed 'moral relativism' - but this term can be misleading.
There is no such thing as moral relativism - what is called moral relativism is actually nihilism.
Relativism entails a stable and permanent reference of morality - otherwise there is not relative, quantitative difference but simply difference.
'Relativism' actually implies that all difference is qualitative (not quantitative - because quantity requires a fixed measure).
In fact, relativism - whether applied to morality, truth or beauty - is a denial of the reality of morality, truth and beauty.
In other words, what is termed relativism is actually nihilism - when nihilism is defined as the denial of reality; since reality must be single, stable and permanent.
Reference: Nihilism by Eugene (Seraphim) Rose circa 1962.