I identify as a politically homeless leftist - meaning, my family left "the party" as those masquerading as "left" and representing the party are immoral charlatans with only their self interest at heart. Political correctness by itself is not something I have an issue with. That is, I have no issue with teaching people what should be common decency.
Bringing up Homer in this context though is extremely intriguing. Because truly reading those classics, not for the "Achilles was a max level fighter wit epic gear" but for the sociopolitical context they give us for the time, is fascinating. The Iliad especially (though later tragedies such as Aeschylus's Oresteia even more so) judges very harshly actions that we now explain away as "those were different times; you cannot judge them by today's values". It turns out, yes, you can. There is no denying that Cassandra is the most tragic character in the Iliad. She spurns Apollo and is cursed by him to see the future but have nobody believe her. She is locked away as a raving lunatic by the people she loves and tries to save. She sits helpless as she watches events that will lead to countless deaths, including her own. And the audience knows this. The audience back then knew that what Apollo did was wrong.
Troy falls and Cassandra seeks protection in the temple of Athena. Ajax the Lesser rapes her regardless. The audience is on her side. It understands that rape is wrong. Perhaps wrong because she was a princess seeking protection of the goddess, where raping a slave girl would have been acceptable, but it is obvious rape wasn't just "just rape". As he isn't punished, Athena kills a lot more people than just him in retribution. Of course, that didn't stop the Locrians of venerating him as their national hero.
Cassandra will later be murdered in Aeschylus' Agamemnon, first of the Oresteia trilogy of tragedies. Which incidentally has a lot to say about violence against women.
Cassandra as the most tragic character shows that there was understanding for subjects we see as new now. Otherwise the audience could not have recognized the tragedy.
But, as my pasta is getting cold, what I am getting at is: the classics have a lot to say about the matters we of the left are interested in highlighting. And they are not just a showcase of a more unenlightened time - these are matters that interested poets thousands of years ago as well. And they had something to say about the matter as well.