I am assuming "morally correct" means "what one ought to do". I thought you had been assuming good was moral (so I had been adopting that premise).
Sorry that I am being a bit stubborn, but Objective Morality is a Term of Art in the branch of Ethics and it is one of the few terms I will insist on using correctly. Objective Morality states that moral statements are either true or false. https://en.wikipedia.org/wiki/Moral_universalism It has nothing to do with people agreeing/disagreeing. It is only about moral statements having exactly 1 truth value.
Does it say everyone agrees whether a particular moral statement is true or false? No.
Does it say everyone agrees that the statement "All theft is immoral." is True? No.
Does it say everyone agrees that the statement "All theft is immoral." is False? No.
What does it say? It says the statement "All theft is immoral." has exactly 1 truth value.
It says if John claims "The statement 'All theft is immoral.' is true." and Jane claims "The statement 'All theft is immoral.' is false." then exactly 1 of them is correct. They can disagree, and did disagree, but only 1 of those meta-statements will be true. The other will be false.
So technically yes. Of all the people that make claims about whether the statement "It is immoral to wear white after labor day" is true or false. Everyone that is correct chose the same answer. Either all true or all false depending on whether the statement actual is true or false. However people can be incorrect too. Objective Morality is not claiming there is a consensus, it is claiming there is a correct answer to statements about morality.
Now, statements about morality also tend to dwell on correctness because moral / immoral are labels for correct / incorrect.
So Shiro Edgelord might agree that wearing white is [Strange]*, the might also believe it is moral or amoral because they think [Strange] is cool. But they would not think it is both moral/right/correct and immoral/wrong/incorrect.
*Using the [Strange] alignment to avoid conflating [Good] with moral.
Now in D&D for the exact same reason for why we don't have a consensus about morality IRL, characters in the game could consider [Strange] to be moral. They could even believe that if they called [Strange] "Evil". They could even do it if the GM called [Strange] evil. They could even do it if the GM said [Strange] was immoral.
Agreed.
For this to be true, the alignments would be orthogonal to rather than coincide with moral/immoral. That is a bit unusual but a possible cosmology. Normally alignments like Good and Evil would coincide with moral/immoral.
So we are back up here again. I already touched on why objective morality does not imply consensus. However if you are divorcing good/evil from morality, then why would Objective morality have anything to do with them?
Ah. When I talk about a topic I use the words from that topic. If I were talking about math I would use the IRL terms for it. I would talk about Binomial Coefficients rather than Grabok's Numerals (fictional example). I would make it clear by Binomial Coefficients I meant the term as defined IRL rather than the Chultian Lizard (fictional example) with the same name. However when I did need to switch between game terms and IRL terms, I would try to make some clear like to avoid overloading a word.
That said if you are not interested in the topic of Objective Morality due to having no interest at this time to delve into that branch of philosophy, then that is good too.
There is plenty of amoral alignment discussion for this thought experiment.
I think Planescape works best if the players/GM don't know what is moral/immoral for that universe. It can work either way but it seems better if the audience is not biased.