This will seem to come, if you will pardon the expression, right out of left field but any honest thinking about moral authority has to consider the legacy of Marxism.
Why? Because Marxism was* devoted to destroying moral authority.
Marx believed that everyone had an ideology formed by the economic system they lived under and the only true “ideology” was the one that would come to prevail after the revolution.
Think about that one a moment. In Marx’s thought there could be no true morality until after capitalism was swept away.
So, how was a good Marxist supposed to have moral arguments? The key to success was to undermine the moral basis of capitalism but it could not be done by appealing to any better morality because the better morality could not exist until after the revolution.
The answer Marx came up with was a particular kind of ad hominem—Marxists accused opponents of being hypocrites. They accused them of not living up to their own moral standards.
The problem with that, of course, is that no one lives up to their own moral standards. The best any of us can say is that we try and you can tell who is trying and who isn’t trying. But saying that you are trying only works if the person you are arguing with is also trying. And Marxists were not trying to live up to any moral standards because they didn’t believe that any worthwhile moral standards were possible yet. They were only interested in undermining the moral standards that supported capitalism and liberalism.
Marx is now in the dustbin of history but that moral legacy lives on. Moral argument nowadays does not consist of trying to defend the truth of certain moral claims. Instead we to undermine the people we don’t like through ad hominem accusations of hypocrisy or we call tem racists or sexist or whatever.
And we argue with prejudice. If someone with a moral belief I don’t like is caught embezzling or cheating on their spouse, well that just proves what is true of all people who believe that. If someone who agrees with me is caught embezzling or cheating on their spouse, well that’s just an individual case.
* My use of the past tense is intentional here. There are still Marxists out there just as there are still flat earthers, Theosophists and Unitarians but these are just eccentricities now. So too Marx is a spent force in history. But all these things used to matter a whole lot and they have left a legacy we still live with.