Hepzibah Pyncheon is different from her cousin Judge Pyncheon in almost every way except for one: she takes huge (and arguably unwarranted) personal pride in her family. Hepzibah seems to believe that she is an aristocrat surrounded by lower-class people. The narrator points out that not only does Hepzibah have nothing much to be proud of in being a Pyncheon, but the whole idea of "gentlemen" and "ladies" belongs to an aristocratic class system that should have died out with the American Revolution.
No matter how wrong Hepzibah may be about her family pride, she truly believes in it: she's willing to become absolutely penniless and desperate before finally caving in and opening her shop in the House of the Seven Gables. And once she actually unlocks the door for customers for the first time, she bursts into tears – what would her grand ancestors think of her working for her living?! Hepzibah's family pride keeps her locked in her cold, empty house for 30 years. Hawthorne is using her example to show the ways in which pride (especially false pride) can be both damaging to other people and self-destructive.
Although the Maule and Pyncheon families seem opposed in every way (in terms of social respectability, wealth, influence, and power), they share the same unbending family pride. It's this shared characteristic that prompts them to fight one another endlessly for 150 years.
Hawthorne is drawing on the Puritan religious idea of the "elect" in his depiction of Judge Pyncheon's notion that his economic success and public respectability prove his moral virtue.