Yes it is, because the rules expects us to have one objective definition.
Of nine different broad moral categories, each of which I can and have created PCs and NPCs for who can passionately defend the correctness of that morality over the other eight. Yes, the rules expect you to have objective definitions of each of the nine ways of looking at the world in a singular framework. But no, the rules have never required you to be single alignment. This isn't like WEG D6 where if you turn evil under the rules definition of evil you become an NPC. This is a game that encourages you to make complex characters of different alignments. And if you are say Lawful Neutral (to pick a culturally very unpopular alignment), the rules don't tell you that you are wrong.
Without that requirement it doesn't matter if people disagree what "good" means.
I think that statement is unintentionally revealing.
Their PCs can debate moral issues in-character like people do in the real life, without anyone having to determine who is "objectively correct."
You mean in real life people don't try to determine who is objectively correct?
Really, the fact that you are still stuck on the idea that if it is called Good it must be objectively correct (which is clearly false) suggests to me that this is a proxy argument for something else entirely. Why is that a sticking point? Do you really think that having "Detect Alignment" would solve moral questions, and most especially that it would solve moral questions in a "Great Wheel" type cosmology of moral peers? Why do you think that is a given how obviously false it is? Do you really think that people in the Great Wheel multiverse cast Detect Alignment on an Archon and say, "Well, that settles my question. He must be right?" Obviously they wouldn't. There would still be the open questions of moral authority - like who has the authority to decide what is right and wrong. And there would still be questions like, "Even if your alignment sounds great, it doesn't actually conform to the world we observes exists. Your alignment only works on paper. It's a pretty but childish fantasy. As practical matter, it only leads to grief."
I don't know you, but I have never played with a person who told me how alignment was too constraining and it meant that there couldn't be meaningful exploration of the concepts of good and evil who in actuality wanted to do any of that exploration. Invariably, they just want to do what that want to do without having to think about it. They aren't interested really in even questioning themselves about "is that what my character would do". Eighty percent of all players in my experience only play themselves through their character. They play the same character in every game and that character has the majority of their personality. And most of those aren't interested in moral dilemmas or exploring philosophical space. They are mostly like, "How can I survive this combat and get the loot?" And I get that. It's a game. Most people play games to win and to hang out.
But really weird thing for me that I don't get is even in the worst case, where your GM insists on defending an offensive definition of good, if you really were interested in exploring morality why couldn't you lean into that? Why couldn't you rebel against the universe? Why couldn't couldn't take on the label of a rebel and say, "If you are the moral authority, then I'm standing against you!" That at least would be interesting and matter. But I really strongly get the vibe from your arguments that the real underlying thing you are arguing for is that it shouldn't matter, and can we get back to the game where we kill things and take there stuff please? Which is fine. That's a perfectly valid way to play. When in groups like that I try to lean into that process of play.