The women in Mansfield Park have a pretty rough time. The only choice most of these women have is to say "yes" or "no" when a guy proposes to them. In fact, it is considered their duty to be married, their future life will depend almost entirely on the man they marry. And if a woman is involved in a scandal with a guy, the woman takes the fall for the affair. Things aren't fair and equal here, but gender rules and roles aren't just about men vs. women. Gender roles are greatly influenced by class, birth order (eldest or youngest kid), and money as well.
Even if Fanny had continued to forcefully refuse Henry's proposal, it would not have done any good because her male relatives were pushing for the marriage. She would have been pressured to marry Henry regardless.
Edmund has unrealistic ideas about how women should behave, as is evident in his treatment of Mary.