Allow me to answer your rhetorical questions. Yes, the Iliad is both a foundational text of heroic fiction and includes belittling, sexist ideas.
This is a really easy mistake to make. You think that noting a moral infraction on the part of a story or picture or representation is an attack on that thing's essential worth. It is not. As any good social theorist would tell you, one can like something, enjoy it, even find it personally meaningful, while still finding fault with it.
For instance, I fucking love Joss Whedon and The Avengers, and Loki calling Black Widow a "mewling quim," old Shakespearean for "whining cunt" is unnecessary and bad. I still love the movie, and I acknowledge that that line was poorly chosen.
It's okay. Art can take it. We grow as a society as we realize our past and present faults. We laud what is good and point out what detracts and distracts from that good in hopes that these distractions will eventually end.
All our most exalted artwork is socially chosen, not objectively, universally, absolutely worthy. Things fall into and out of style. Rejecting moralistic criticism of art is rejecting morality itself.
Speaking for myself, I want to love things unconditionally. I want Bioshock Infinite to be a masterpiece without fault. But that desire should not cloud my judgment.
There is no danger in criticism. There is only growth.
Should the Iliad have points docked for being sexist? Would Dracula cease to be a masterpiece if the vampires and Renfield were black, while the rest of the cast remained white? Are we supposed to quit admiring the works of all the great painters throughout history on account of the inequality at display in their art? Would the paintings of Sir Leighton be better if they depicted more black people? Is Rubens' Rape of the Daughters of Leucippus worse because contemporary morality condemns its subject matter? Or Gérôme's Slave Market in Rome?