Sexism

Sexism was the idea that all members of one gender were superior or inferior to another.

By humans
Sexism could be found throughout human history, towards both women and men.

Women in the early 17th century were often suspected of witchcraft and burned or drowned for it. Otherwise, woman were frequently regarded as lesser than their male counterparts at best. Indeed, the Thirteenth Doctor remarked that this era was a hard time for women because "when we’re not being drowned, we're being patronised to death". (TV: The Witchfinders)

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

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

One professor in 1963, Professor Garland, held that women were not suited to serious academic study, as "they tend[ed] towards emotionalism" and lacked the necessary "temperament". He promoted a far less skilled employee at the National Museum, Timothy, over Helen Sinclair. (AUDIO: The Red Lady)

Some women would casualty make sexist remarks as Peri Brown believed that men were incapable of explaining simple mechanics (PROSE: Attack of the Cybermen) and River Song thought that it "looked weird" when a man was thinking. (TV: The Husbands of River Song)

On the Inferno Earth sexism was a major social faux pas by the 1970s. (TV: Inferno)

In the Daft Dimension, by 1971, "1970s racist and sexist" flavour crisps were being sold. (COMIC: The Secret History of Life Before Doctor Who Magazine!)

Also in the Daft Dimension, the Daleks had a variant called the Sexist Daleks, which they deployed as a countermeasure when they discovered that the Doctor would become a woman. (COMIC: The Daft Dimension 517)

The Doctor
Compared to, and to the embarrassment of, his successors, the First Doctor held some mildly sexist attitudes. When he first met Tegan Jovanka during the Game of Rassilon, he assumed that she got refreshments for his future self, the Fifth Doctor asking his companion to humour his younger self's quirks. (TV: The Five Doctors) At the end of his life, the First Doctor crossed paths with the Twelfth. Initially doubtful that the man was his future self and not liking him, the First Doctor deliberately exaggerated his attitudes to annoy and embarrass his future counterpart. As he grew to approve of the Twelfth Doctor, he abandoned these remarks. (TV: Twice Upon a Time, PROSE: Twice Upon a Time)