Austen knew and shared Wollstonecraft's sentiments as expressed in A Vindication of the Rights of Women.
Despite being perceived as a radical document in its day, Wollstonecraft's Vindication is not "feminist" by modern standards. Its main argument is that women should be better (and more rationally) educated so that they can be better helpmeets to their husbands and mothers to their children. Wollstonecraft does not advocate that women should work outside the home, live independently, or have the right to vote: she sees women's place as firmly imbedded in the home.
In Sense and Sensibility, Austen also shows she believes that women should be firmly imbedded in home and family. The novel, like A Vindication, shows the problems that arise when women are not educated to be rational, thoughtful people who exercise good sense. Lucy Steele, for example, has been taught to be a duplicitous husband-hunter who will shamelessly lie and manipulate others to get her way: this is exactly the kind of all-too-common female "education" that Wollstonecraft objects to, claiming that it leads to unhappy marriages and homes.
Likewise, Mrs. Dashwood is too indulgent of her favorite daughter, Marianne, and doesn't educate her to use good judgment. This leads Marianne to live an overly Romantic and self-centered life, including believing Willoughby will marry when he has given no concrete indication he plans to do so. Marianne's extreme sensibility or emotionalism leads her to overreact to the point of a life-threatening illness when she discovers Willoughby is planning to marry another woman for money.
Many of the women in Sense and Sensibility are silly, vain, and competitive with other women—these are all traits Wollstonecraft attributes to the frivolous way women are raised and educated to be childlike and lacking in moral fiber. Austen illustrates through her novel that this way of being a woman is not helpful to the larger social order.