Purity

Purity was a state in which something was free of all impurities.

Daleks
The Thirteenth Doctor observed that the Daleks were "pretty obsessed" with purity, ironically for a species born out of mutation. (TV: Revolution of the Daleks) The Eighth Doctor noted that the pitfall of such a belief was that different factions of Daleks had different definitions of purity. (AUDIO: Restoration of the Daleks)

Nyder believed that the Kaled race must be kept pure as he explained to the Fourth Doctor that the Mutos were rejected. The first Daleks created by Davros deemed their humanoid progenitors to be an inferior species and so saw to the extermination of the remaining Kaleds with the Dalek Prime opening fire on Davros himself. (TV: Genesis of the Daleks)

Ace understood that the warring Renegade Daleks serving the Supreme Dalek and the Imperial Daleks of Davros hated the other for their differences, the latter group being "blobs with bits added". (TV: Remembrance of the Daleks)

The Daleks of Skaro deemed a new race of what they called Mutant Daleks, created by Professor Martez on Red Rocket Rising, to represent a "deviation from the purity of the Dalek bloodline" and so saw to their extermination. (AUDIO: Blood of the Daleks)

As the Last Great Time War persisted, the Dalek ideals of racial purity were weakened. A Brief History of Time Lords claimed the Cult of Skaro were a result of this, (PROSE: A Brief History of Time Lords) though the members of the cult were known to be "pure" Daleks. (TV: Daleks in Manhattan) A group of the Dalek Scientific Division sought to restore the Daleks to a humanoid form, ignoring orders to stop over concerns of purity. (AUDIO: A Thing of Guile) Towards the end of the war, Daleks of human origin were created to bolster Dalek forces and were viewed as expendable "cannon fodder" to their Kaled mutant counterparts. (PROSE: Engines of War)

The Dalek Emperor in the Last Great Time War insisted that his Daleks of human origin were not "half-human", an observation from Rose Tyler which he found blasphemous. He claimed that everything human had been purged from them, that he had "cultivated pure and blessed Dalek." Nevertheless, the Ninth Doctor observed that these Daleks hated their own existence. (TV: The Parting of the Ways)

Dalek Sec noted that a pure Dalek was intelligent but emotionless. To the Tenth Doctor's shock, Sec voiced his belief that Davros was wrong to remove emotions from the Daleks. (TV: Evolution of the Daleks)

Before their near-extinction at the end of the Time War, the Daleks created thousands of Progenitors containing pure Dalek DNA. A Dalek ship, the last survivors of the New Dalek Empire created from Davros' body, (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) found the last remaining Progenitor, which deemed them to be impure, forcing them to goad the Eleventh Doctor into providing his testimony, verifying them as Dalek and so enabling the Progenitor to create a New Dalek Paradigm, the first members of which disintegrated their "inferior" and "unclean" predecessors who accepted their extermination. (TV: Victory of the Daleks)

When inside Rusty's casing, the Twelfth Doctor pointed out the Dalek's cortex vault, noting to his companions that it was what kept a Dalek "pure". (TV: Into the Dalek)

Knowing that the cloning process which resurrected the Reconnaissance Dalek and created the New Dalek Army resulted in them containing trace amounts of human DNA, the Thirteenth Doctor signaled the Dalek Death Squad spacecraft knowing that they would exterminate these new Daleks thus stopping their attack on Earth. (TV: Revolution of the Daleks)

Others
Throughout his reign, Rassilon had championed "Time Lord purity". Following his being deposed however, he was quick to abandon his belief upon allying with the Cyberiad and becoming the Cyber-President. (COMIC: Supremacy of the Cybermen)

Following the Great Intelligence corrupting the Doctor's time stream, Strax reverted to the mindset of a typical Sontaran soldier and attacked Vastra, deeming her an "affront to Sontaran purity". (TV: The Name of the Doctor)

In the far future, Cassandra O'Brien.Δ17 considered herself to the be the last pure human, as the rest of the species had evolved and/or mated with alien lifeforms. (TV: The End of the World) Despite Cassandra's dislike of her, she also considered Rose Tyler to be a pure human. (TV: New Earth)