TNG 5x17 'The Outcast': An androgynous race prohibits any expression of gender, as it is viewed as 'primitive'.
TOS 3x15 'Let That Be Your Last Battlefied': Two members of the same species view the other as inferior because of which color is on which side of their body.
VOY 7x13 'Repentance': Voyager rescues passengers from a prison ship whose prisoners are on their way to be executed.
TNG 2x9 'The Measure of a Man': Data's sentience is brought into question when he is forced by Starfleet to undergo an undesired procedure.
TNG 7x20 'Journey's End': The Enterprise is ordered to relocate a population of Native Americans from their planet of 20 years because of a treaty with the Cardassians.
ENT 2x14 'Stigma': T'Pol is recalled when it is discovered she has Pa'Nar syndrome, a disease transmitted through mind-melds conducted by an unaccepted sub-culture of Vulcans.
DS9 6x13 'Far Beyond the Stars': Benny Russel is fired from his writing job when his story about a black space station commander receives scrutiny from the publisher.
TNG 7x9 'Force of Nature': Two Hekarans board the Enterprise to convince them that their warp drive is damaging their home world and the space around it.
TOS 1x23 'A Taste of Armageddon': The Enterprise discovers a 500 year war on a planet that is run by computers that calculate the fatalities and force those people to die.
VOY 3x6 'Remember': B'Elanna experiences the memories of a telepathic woman's youth, where her lover and his people are relocated and murdered without repercussion.
Star Trek + Social Commentary (context in the captions)