It is arguable that Hillary has been fighting a type of "establishment" all her life because of her gender, all the way back to when she was first lady of Arkansas and there was disapproval of her keeping her last name and practicing law instead of arranging flowers and hosting dinner parties (
https://www.youtube.com/watch?v=LMIoYihU7VU). When Bill ran for president. she was questioned endlessly about her decision to practice law during Bill's time as governor, and when she made a frustrated (and politically unsavvy) remark about not wanting to be a housewife, she was forced to release a chocolate chip cookie recipe (
http://clinton2.nara.gov/WH/EOP/Firs...l/cookies.html). Although women's equality have definitely progressed since then, this is the type of establishment and status quo that Hillary is referring to when she says that being the first female president is against the establishment. It is not the same establishment as what Bernie is referring to.