I am a moral relativist but not a cultural relativist or a "garbled relativist". I am a moral relativist by default. There is no absolute, apodictic, unchanging, eternal, universal moral law that we all have access to and that everyone can agree on without dispute, something analogous to mathematics. Or an absolute authority that everyone can recognize regardless of differences in personal belief. Some may claim to be in possession of such but of course others will not agree and there is no way to past both sides claiming “I’m right and you’re wrong”.
I edited this to add:
This is not to say that as a relativist I hold all moral claims, judgments, and actions to be no better or worse than any other, but only that the determinations we make are not based on an objective standard. We need to deliberate together in order to determine what seems best, leaving it open to revision over time.