"Everyone" also isn't quite right, as there are many evil races that wouldn't normal[l]y cooperate in such cases. A simple filter for this would be of[f]icial playable races that are (mostly) neutral or good aligned, so excluding races such as orcs and goblins.
Well, "sentient", "mortal", and "raman" have nothing to do with morality; "civilized" and "society" only concern morality under their 19th-century imperialist senses (at which point you're treading water around "Are we the baddies?"); and "free peoples" and "free folk" work in context if you're contrasting it with a slave or fascist state but better suit situations like Mr Martin's, where anarchic badlands are being contrasted with kingdoms and hierarchical leadership of any sort.
"The Good Races" may catch in an American or German throat, but this is a world where alignment is real to the point of being physically detectable.
Collective adj. The good people, collectively.
is a fine way to refer to those who are not selfish or evil. (Here is one example in the wild.) Similarly, you could go with "the Good Peoples of the Realm/Plane/Multiverse/whathaveyou".
If you want to pick the nit that PC races can and often are selfish or evil as individuals, you could do something silly like calling them "the Good-Capable", "the Possibly Good", &c. or something religious like "the Savable", "the Redeemable", &c. or something bitter and Po-Mo like "the Notionally Good", "the So-called Good", &c.
Really, though, you're defining the boundary between the people you consider people and those you consider monsters. If you don't just want to go classic "Us" versus "Them", just use the base words
"the Folk", &c. You could object that such terms are too broad. They aren't. Any race your LG paladin can slay on sight—whose children your LG paladin could slay on sight—with alignment impunity isn't considered an actual race of people in your game, but some kind of varmint, pollution, pestilence, &c. to be removed for the actual decent folk of your world.