The Githyanki had the help of Tiamat and the Red Dragons
InOn MM pgp. 159, it is mentioned that the githyanki are Red Dragon Riders -- that, in the uprising wherein they overthrew their Illithid masters, their leader Gith's advisor, Vlaakith (their now lich-queen ruler), sought the help of Tiamat. As a result of these dealings, Tiamat's partner Ephelomon accompanied Gith back into the Astral Plane, declaring that all of his allies willwould be allies of the githyanki as well, forever.
Not all Red Dragons honor this alliance, but at least, most of them don't consider githyanki as enemies. And it is strongly implied that even to this day, githyanki are still Red Dragon Riders.:
The githyanki plunder countless worlds from the decks of their astral vessels and the backs of red dragons.
Note that the bolded word is in present tense. They are still plundering countless worlds from the backs of red dragons.