Was Jane Austen influenced by Mary Wollstonecraft?
While we can't know for sure, I would say it is highly likely that Jane Austen read and was influenced by Mary Wollstonecraft. For evidence of that, I would point the reader to Miriam Ascarelli's 2004 piece in Persuasions discussing feminist connections between the two writers (I would object, however, to Ascarelli's characterization of Vindication as strident and rambling).
While Ascarelli notes similarities between Austen and Wollstonecraft in terms of women's education, Ascarelli also points to actual links between Wollstonecraft and the Austen family:
Austen biographer Claire Tomalin offers some convincing biographical evidence that Austen is likely to have known of Mary Wollstonecraft and her work. She notes that Sir William East, the father of one of George Austen’s former pupils, was a benefactor of Wollstonecraft. Furthermore, Sir William was a neighbor and friend to Austen’s uncle, James Leigh-Perrot. After Wollstonecraft attempted suicide in 1796, Sir William was credited with being particularly kind to her during her recovery. While this does not specifically link Austen and Wollstonecraft, it makes it plausible that the Austen family knew of Wollstonecraft and her ideas.
Beyond that, Austen was an extremely well-read woman. Her novels also show the troubles that a lack of good education can cause for a woman, such as Emma Woodhouse. Further, as Ascarelli and other critics have pointed out, the period in which Austen was writing was one of censorship. England has never had a First Amendment guaranteeing freedom of speech. During a time of war with France and heightened sensitivity to the idea that radicals might be secretly helping the French, writers had to be very careful what they said. Since people like Wollstonecraft were in disrepute, Austen would have had to quietly weave a critique of women's education into her novels, which she does.
This is a good question. In terms of dates, it is not impossible that Jane Austen would have heard of Mary Wollstonecraft or encountered some of her work. On the other hand, there are several factors that make direct influence improbable.
For 21st century readers, both these writers fall into the category of late 18th/early 19th century female authors, and both may be studied together in classes on women’s literature and often read from a feminist perspective.
From a 19th century perspective, Mary Wollstonecraft was a scandalous woman who had two illegitimate children. Respectable women would not associate with her or read her work. Jane Austen was a clergyman’s daughter and outwardly conventional. In Northanger Abbey, we get a sense that although she sees a single young woman riding in an open carriage with a man on Sunday as more imprudent than immoral, she thinks such behaviour best avoided. We don’t see evidence that she approved of any radical ideas (or of radicalism as a mode of action) , but like many latitudinarians, would have argued that better education for women (e.g. reading Addison and Blair rather than Anne Radcliffe) would make them better members of society and better Christians.