There are two senses in which critics categorize Austen and Pride and Prejudice as conservative: (1) as socially conservative, which includes class divisions; (2) as politically conservative, which includes women's rights. The definition of conservative that is applicable combines two meanings: "preserving established customs"; conventional, traditional, resisting change (Collins Dictionary). When critics like Julian North (quotation above) call Austen and Pride and Prejudice a "conservative" author and text, what is meant is that she does not attempt to stir social reform to the existing social class system or any other institution (e.g., marriage) or custom, unlike Charlotte Brontë (Jane Eyre, 1847) or Charles Dickens (e.g., Little Doritt, 1857).
One textual support for the idea of conservatism is that Elizabeth's initial emotionalism is overruled by reason (a favorite theme since her juvenilia) when she accepts Darcy and enters a marriage that represents the social and class ideal: poor upper class gentleman's daughter marries wealthy upper class gentleman's son. Another textual support is that Charlotte, who is the story's voice of reason, yields to practical social realities and marries Collins for economic and social class advantage, not for love.
I hope you will be satisfied with what I have done. I am not romantic, you know. I never was. I ask only a comfortable home; and considering Mr. Collins's character, connections, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast
A third support is that Lydia and Wickham are forced by Darcy and Uncle Gardiner, at great monetary cost, to become respectably married; this preserves the entire family from social class disgrace and ostracism though at great personal cost (the family connection with Wickham is onerous and the drain on income).
For a fuller understanding of the issue, three opposing arguments against conservatism are implied in Pride and Prejudice. The very act of writing and publishing is a form of action for women's reform. Women were not accepted as having high intelligence and understanding, which makes Sir Walter Scott's assertion of Austen's genius even more meaningful than otherwise. For a woman to take action and go against the conservative reality--like Austen and Fanny Burney (Evilina, 1778) and Ann Radcliff before them and Charlotte Brontë after them--was an implied protest against conservatism and affirmation for reform.
Another argument against conservatism is the implied protest against class order evident in Elizabeth's rebellion against marriage to her cousin and against her parents' express interest and wishes (at least her mother's wishes, though one must suppose that, though saying otherwise, Mr. Bennet would not be unhappy to know his early wasteful ways were redeemed and his widow and daughters would be provided for because of a marriage to the recipient of the entail, Mr. Collins).
Another argument against conservatism is the implied protest (1) against entails of wealth and property away from women and (2) against restricting women's power and authority: whatever haughty things Lady de Bourgh might be, she is wealthy and powerful in her own right because the males in her family line recognized women's value, competence and worth and protected her wealth, status and authority through available legal means.