Racism

Racism was the idea that all members of a race were superior or inferior to another race. An individual with this belief was known as a racist. (TV: Oxygen, Rosa) Some words used to humiliate other races were also described as racist. (TV: Remembrance of the Daleks, Human Nature / The Family of Blood)

By humans
While visiting Regency London in 1814, Bill Potts was subjected to racist (as well as sexist) remarks from Lord Sutcliffe, referring to her as a "creature" and demanding she "show respect in the presence of [her] betters". The Twelfth Doctor responded by punching him in the face, knocking him down. (TV: Thin Ice)

While Martha Jones was working as a maid at the Farringham School for Boys in 1913, Hutchinson made several racist remarks to her, and Joan Redfern showed disbelief that a woman of her "colour" was really training to be a doctor. (TV: Human Nature/The Family of Blood) She also feared that she would be carted off as a slave in Elizabethan England. (TV: The Shakespeare Code)

In 1941, during the Second World War, 21st century native Toshiko Sato was insulted by Americans in the Ritz dance hall because she was Japanese. (TV: Captain Jack Harkness) In the same year, when Clyde Langer told Nazi SS officer Koenig that he did not belong in England, he remarked that that was "quite a statement for a negro". (TV: Lost in Time)

Segregation of black people was rampant in the United States of America in the 1950s, in which black people were required by law to use separate facilities to the whites, particularly in Southern states like Alabama and Mississippi. These policies were in place from at least 1943. On 1 December, 1955, while travelling home from work, civil rights activist Rosa Parks famously refused to give up her bus seat when the bus became crowded, leading to her arrest, an event that the Thirteenth Doctor, Ryan Sinclair, Yasmin Khan, and Graham O'Brien witnessed. Her arrest lead to the Montgomery Bus Boycott, and a further chain of events that would result in the abolishment of segregation a year later. (TV: Rosa)

Mexicans and those of Mexican heritage were also segregated in America during the 1950s. Yasmin Khan was mistakenly perceived as Mexican in a Montgomery diner so was denied service. She also had to discretely enter a "whites-only" motel because of this prejudice. However, she was permitted to enter through the front door to board a segregated bus and could use the "white" seating area. Such mixed treatment caused Yaz to remark she was unsure of her place in Montgomery given the scarce number of people of Pakistani heritage in the city. (TV: Rosa)

As well as segregation, black people suffered racial violence in the 1950s. After Ryan Sinclair attempted to return the glove of a passerby, Lizzie, he was slapped by her husband and ordered to get his "filthy black hands" off his wife. The husband alluded to Ryan being lynched were he to disturb a woman in Montgomery. After Rosa Parks calmed the man, she explained to the Thirteenth Doctor, Ryan, Yasmin Khan and Graham O'Brien that outsiders were not safe in Montgomery. Having read about the death of Emmett Till in the newspaper, she explained that the northern Till was found dead in a river after a "couple words to a white woman" while he was on vacation in Mississippi. (TV: Rosa)

In 1963, a sign hanging in the window of Mrs Smith's Shoreditch boarding-house read "NO COLOUREDS", which Ace seemed to be disturbed by, so she took it down and hid it. (TV: Remembrance of the Daleks)

The house of Ace's friend Manisha Purkayastha was firebombed by racists in 1983. (TV: Ghost Light)

In 2009, when Wilfred Mott remarked he was saved by the cactuses, the Tenth Doctor replied with, "That's Cacti", to which the Vinvocci exclaimed that it was racism. (TV: The End of Time)

In the 21st century, Sheffield, racism existed on a lesser scale than that of the 1950s, bearing a massive difference. Graham O'Brien, Ryan Sinclair and Yasmin Khan were visibly appalled at the difference. While not physically assaulted as he was in the past, Ryan Sinclair still remarked he would be stopped by the police more often than his white peers, while Yasmin Khan suffered racial slurs such as "paki", and "terrorist" because she was a Muslim. (TV: Rosa)

Freda's house was burnt down by racists in 2069 because of her alien mother. She was saved by a member of Torchwood, who sent her back in time to 2009 via the Rift. (AUDIO: Asylum)

Roz Forrester found it difficult to understand the racism and sexism she experienced in 1919 Paris since such attitudes did not exist between humans in the 30th century from where she came. (PROSE: Toy Soldiers)

By the 79th century, there were still racists such as Krasko who expressed a desire to alter the history of Ryan Sinclair's "kind", attempting to prevent Rosa Parks from the arrest that would begin the Montgomery Bus Boycott and lead to the end of segregation. (TV: Rosa)

Dahh-Ren briefly branded Bill Potts a racist after the latter expressed surprise at his blue skin. (TV: Oxygen)

On an infirmary base at the North Pole, when Santa Claus and his two elves entered, Santa said it was an invasion, to which Clara Oswald jokingly said "an invasion of elves" to which the elf Wolf said it was racist, and the elf Ian rebranded it "elfist". (TV: Last Christmas)

Amongst other species
Racism in non-humans is probably most notable in the Daleks, whose whole existence was defined by their utter hatred of anything non-Dalek, believing themselves the supreme beings. Their belief in their innate superiority and need to maintain their racial purity was so intense that it led to inevitable conflict between the Imperial Daleks and the Renegade Daleks. As Ace succinctly put it, "They hate each others' chromosomes. War to the death." (TV: Remembrance of the Daleks) Dalek individuals would even become self-loathing if their genome was in some way altered, such as the one in Van Statten's museum, and even drew a line between the very mild differences between Kaled and Dalek DNA. (TV: Dalek, Victory of the Daleks)

Time Lords had become hated by the universe due to the Time War. Cass instantly hated the Doctor when he told her he was a Time Lord, refusing to be rescued by him and telling him to go finish destroying the universe, despite his claims to have never fought in the war. (TV: The Night of the Doctor) Even Clara Oswald was disgusted with the Time Lords, calling them monsters who had to hide out at the end of time because the rest of the universe hated them. (TV: Hell Bent)

The Doctor did not tolerate racism against their companions. (TV: Thin Ice, Rosa) Susan Foreman saw no issue with Lloyd Walker being black and assured him that her grandfather held no prejudices based on skin pigmentation. (AUDIO: An Unearthly Woman)

According to the Fifth Doctor, the Pakhars found the term "rodent people" extremely offensive, even racist. (AUDIO: Nekromanteia)

Jeff Shrubb was accused of stirring up racism, sexism and homophobia on Olleril. (PROSE: Tragedy Day)

The Raxacoricofallapatorians became resented by their fellow Raxas Alliance members in light of the crimes committed by the family Slitheen. Gleda Ley-Sooth Marka Jinglatheen was branded "Raxacoricofallapatorian scum" by a native of Raxacoricovarlonpatorius. (COMIC: Doctormania)

The "Abzorbaloff", a native of the planet Clom, took offence when the Tenth Doctor questioned if he was from Raxacoricofallapatorius. Branding their people as "swine", the Abzorbaloff proclaimed "I spit on them" before revealing that his world was their twin planet. Before that, he ranted to humans that his form was "better than that crude pink shape [they] call[ed] a body." (TV: Love & Monsters)

Behind the scenes
The Black and White Minstrel Show was known for its racism in the 1970s. Controversially, Alpha Centauri made a guest appearance in 1972.