Rudolph could stand in for many people suffering from prejudice. Examples: African-Americans or Native Americans (among other groups) in a white-dominated society; minority religions, women in a man’s world. But the story of Rudolph seems to fit the plight of gays best.
Consider how his father Donner and Mrs. Donner (she’s not given a name of her own, the cartoon’s debut being 1964) hide his ‘noncomformity’, as Sam the Snowman puts it. They use a false black nose to hide the red one. It’s tougher to hide a person’s color, though extremely light-skinned blacks in American history sometimes ‘passed’ for white. Women hid their gender in certain situations, but it’s still tricky to pull off. You could hide your religion, but Rudolph would most likely be his parents’ religion. So being gay works best.
Consider that Rudolph openly demonstrates his potential to be a great flier for Santa’s reindeer team, but is immediately crossed off the list when his red nose is revealed. He’s also banned from participating in any reindeer games, and name-calling is encouraged: gay-bashing of the verbal kind. Fireball, Rudolph’s friend, backs away in fear and revulsion when his red nose is revealed, a straight male’s reaction to discovering his buddy’s gay. Clarice (a beard?) can’t be seen with a ‘red-nosed reindeer’ anymore. This immediate dismissal despite showing that he can do the job of becoming one of Santa’s reindeer simply for having a red nose parallels gays’ situations in the military, and Santa runs Christmastown like a military operation, LOL.
Hermie the Elf doesn’t fit in, either. He’s stuck in a regimented occupation of toymaker, but he doesn’t like to make toys! He doesn’t look like the other elves, either (who always remind me of Vulcans, heh heh). He wants to be a dentist, but his supervisor says he’ll never fit in. So, with his delicate features and pixie boots, off he goes! ;)
He and Rudolph meet and become friends, leaving Christmastown behind (odd that Christmastown doesn't embrace a shiny red nose, considering its love of sparkle and glitter, heh heh), and meet up with Yukon Cornelius, who doesn’t seem to care what they are. They are chased by the Abominable Snowman, who could represent prejudice in general, or organized hate groups (the right-wingers who actively try and keep gays oppressed), and eventually end up on the Island of Misfit Toys.
The Misfit Toys all have something ‘wrong’ with them: a cowboy who rides an ostrich, a train with square wheels on his caboose, a bird who swims instead of flies, a boat that can’t stay afloat, a water pistol that shoots jelly instead of water, a spotted elephant. Admittedly I wondered as a kid why Charlie-In-The-Box just didn’t change his name, and never could figure out why the gingham-dressed girl doll was there. Though I call her Mary Ann, considering she says, “We’ll never get off this island!” and Gilligan’s Island debuted the same year as Rudolph, 1964. ;)
The Misfit Toys could represent the outcasts of society: the disabled, the poor, the elderly, all shunted away out of sight and mind (hospitals and nursing homes) while yearning for ‘normalcy’. But Rudolph and Hermie are misfits among the misfits! Which rings true, because even outcasts scorned gays quite often.
Eventually the residents of Christmastown realize they were being hard on the misfits, even Santa, who had a blind spot about Rudolph’s red nose, symbolizing even otherwise-good people discriminating against gays when they would be horrified to be called a racist or intolerant of religion.
The gay-bashers end up toothless (the Bumble ends up without teeth courtesy of Hermie and is rendered harmless) and Rudolph saves the day, considering it an honor to lead Santa’s sleigh. Hermie gets to be a dentist (does he rock those pixie boots or what?), the Bumble gets a job putting the star on the top of the Christmas tree, and even the Misfit Toys find happiness! :)