There are various flavors of moral relativism. My comment criticizes one flavor of moral relativism without specifically identifying that I was criticizing meta-ethical relativism.
> Descriptive moral relativism holds only that people do, in fact, disagree fundamentally about what is moral, with no judgment being expressed on the desirability of this.
> Meta-ethical moral relativism holds that in such disagreements, nobody is objectively right or wrong.
> Normative moral relativism holds that because nobody is right or wrong, everyone ought to tolerate the behavior of others even when large disagreements about morality exist.
> Said concepts of the different intellectual movements involve considerable nuance and aren't absolute descriptions.
Quotes from Wikipedia [1], even though I prefer the Stanford Encyclopedia of Philosophy [2] for more detailed explanations.
[1] https://en.m.wikipedia.org/wiki/Moral_relativism
[2] https://plato.stanford.edu/entries/moral-relativism/#ForArg
Moral relativists can have moral beliefs. They simply recognise that these are their own (very strongly held) opinions, rather than a reference to a universal moral code (like say, the Ten Commandments)