[kirse]

But was there ever an objective basis?

People certainly behave in ways that reflects there is an objective basis to be reached - they argue about correctness of perspectives, attempt to reduce complex formulas to the simple, have entire reasoning + discovery systems (science) designed to reach the truth, etc.

I have yet to meet someone who truly dogfoods their own supposed beliefs on a "relative morality". You'll often find those people claiming all truth is relative, but are equally willing to argue ad-infinitum on whether they think you're right or wrong on a certain topic.