I believe there were multiple cyclopes in mythology, not just the one that Odysseus encountered.
Also, Medusa was one of the Gorgons. I guess E. Gary Gygax didn’t know that.
“Pegasus” definitely was a specific individual whose name is now used generally to mean a class, “winged horses.”
It varies depending on what era of history the myth came from, but generally they’re portrayed as a species, or at least a family.
Dont be silly, Gorgons are big metal infernal cows! 
They were clearly Romans, the name, the rank titles, etc.
Hardly typical.
D&D has typically embraced modern western liberal notions of individual freedoms throughout it editions. In good kingdoms, you could count on the right to freely worship your god of choice, the rule of law prevails, the state will respect your property, and the negatives we associate with feudalism simply don’t exist. But in some settings we might not be dealing with feudalism at all. I don’t believe Baldur’s Gate is run monarch but instead an oligarchy.
That can’t be right. Nobody hates cyclops.
Got to love 3000-year-old jokes.
A race (actually, possibly multiple groups.) The individual most people think of actually had a name - Polyphemus.
That’s true. For one, unlike most European medieval societies, in D&D worlds commoners - such as most adventurers - are allowed to bear arms and armor openly and move freely from place to place.
The people to whom Polyphemus was crying out for help, “Nobody is killing me!”, were other cyclopses.
And you can’t lay the gorgon thing at Gygax’s feat. Like so much else in the Monster Manual, the gorgon as metal bull breathing hazardous gas was from medieval bestiaries.
This is actual “woke” culture in D&D. Finding out the original source for Monster Manual entries. Still don’t know if the OP thought it was a problem.
Here is an excellent deep dive by Keith Baker the author of the Eberron campaign setting into the way goblinoids work in that setting. It isn’t meant as any kind of commentary on race or D&D or anything like that - it’s meant for GMs running a game in Eberron. But I think it’s an excellent example of how goblins with culture and history can be far more interesting than “evil orange dudes for you to fight” without being “humans in hats” either.
In this case, the inherent difference between humans and goblinoids is that goblinoids (who are a collection of three related but very different “races”, the goblins, hobgoblins, and bugbears) is that goblinoids were almost eusocial - that their war with extraplanar invaders destroyed these eusocial bonds in most of them - and that this is what led to the collapse of their empire.
Very nice. I always put at least one hobgoblin empire in any D&D world I build; this could be useful in fleshing them out.
The last time I ran a D&D campaign, which was about 10 years ago, I changed up most of the playable and non-playable races, not out of a particular desire to be woke, but because I had decided that Tolkien and Gygax had become boring and predictable. 
(New controversy, eh?) I read Tolkien in the 1970’s and have played every edition of D&D since then as well. I wanted to do something different than use the same tropes that show up over and over and over.
Rather than have the players be able to use their meta-knowledge of those tropes and immediately be able to say “She’s good” or “He’s an obvious villain”, I extended the concept of the Seelie and Unseelie Fey from Celtic mythology. All the sentient or humanoid species came in “good” or “evil” (or neutral) flavors, and weren’t visually distinguishable from each other except through the behavior they displayed. The campaign took place in an alternate history version of the Earth where myths were mostly true, magic worked, and discrimination based on race or sex was greatly diminished. (I assume I didn’t do a perfect job of this.) The players mostly stayed in the vicinity of Constantinople, which was a big melting-pot city. They could be from anywhere in the world.
D&D critters that had no basis in mythology prior to 1000 AD did not exist. Orcs referred to carnivorous Norse or Germanic sea-giants, which is where the word “orca” for killer whales comes from. There were no gnomes. Paracelsus invented them in the 15th century as a personification of the alchemical element “earth”. There were no hobbits/halflings.
I didn’t invent any new game mechanics, but re-purposed the existing mechanics for the various fantasy races. The stat block for gnome characters instead went to the smaller fey such as leprechauns or redcaps (evil leprechauns who wear hats that have been dipped in blood). The stat block for hobbits/halflings went to brownies/hobgoblins (good) or goblins (bad), who again were just two sides of the same coin. Etc.
Eventually, I started playing Savage Worlds instead of 4e D&D, but used the same world for a “Savage Fantasy” campaign. I haven’t used this setting with 5e D&D. Yet.
You should check out The Design Mechanism’s Mythic Britain and Mythic Constantinople sourcebooks. They’re written for their in-house Mythras ruleset (which is essentially their evolution of RuneQuest and by extension Chaosium’s Basic Roleplaying (BRP) system) but they contain a lot of background material and content essentially independent of the game mechanics that could be adapted into any system. The core campaign in the Mythic Britain sourcebook is a less mythologized version of the Arthur legend circa AD 475-550 (i.e. post-Roman Britain) but they also have extended material on general Celtic life as well as the Saxon invasions (and the Germanic culture they brought with them) from AD 495 onward, and the Mythic Constantinople, while set in the 15th Century trade and political intrigues give some good source material going back to the beginning of the proceeding Byzantine Empire.
The Mythras system uses a Passions mechanic which gives the characters specific interests or pressures (if they go with or for their stated Passion) rather than a generic “alignment” mechanic, and this too could be adapted to any system with a little futzing. Mythic Britain is particularly interesting because the Brythonic Celtic culture that predominates pre-Norman Britain was notably egalitarian in many respects (although how much this is exaggerated for the purpose of the game is subject to debate) and it is just as easy to play a female character in that narrative world as a male one (with certain constraints; obviously no overt female Catholic priests, but warriors, druids, and other traditional roles are generally gender-neutral).
Stranger
Those sound interesting! I recycled bits and pieces from the Celts Campaign Sourcebook and Vikings Campaign Sourcebook, the Al-Qadim and Oriental Adventures settings, and a Byzantine setting called The Last Days of Constantinople, all of which were for earlier editions of D&D.
The one prejudice I did deliberately use was the Byzantine propensity for being snobs toward anyone who could not speek Greek or Latin. The native residents of Constantinople were known for often considering other languages a sign of being an uncultured boor. They claimed other languages sounded like the sound of sheep “baa, baa”, which is where the term barbarian comes from.
I remember back when Mayfair games published D&D modules and they did deep dives into classic mythology and then-popular fantasy series with their Role Aids supplements.
One volume was titled Wizards, and they had magic users such as Merlin, Morgan LeFay, Aahz and Skeeve, and Lythande (from Thieves’ World) written up in D&D stats. Each wizard had a scenario beginning with a writeup about their background and noted accomplishments. The players would accompany these wizards in an adventure, and then things would go tits up and the players would have to rescue the wizards. By the end, the wizard would claim credit if the players were successful.
Since D&D always stuck with their own mythology, it was cool to see D&D mechanics applied outside the box. Eventually, TSR would allow open source licenses so other fantasy worlds such as Wheel of Time and Lovecraft Mythos could be adapted.
Not always - they licensed Fritz Lieber’s Lankhmar stories in the 1980s.
Huh. I used to have a friend named Aahz. I’m nearly certain it wasn’t the name his parents gave him, and I wondered what the source was.
(Sadly, he died recently.)