Is it permissible for a Hanbali woman to seek a fatwa from a Shafi'i mufti on a jurisprudential issue, or is it obligatory for her to seek a fatwa from a Hanbali mufti?

An ordinary Muslim is not obligated to adhere to a specific madhhab (school of thought); rather, they may move between madhhabs, provided that this is not done out of mere caprice. So, one may not adopt a madhhab simply out of desire or by imitating what their ancestors followed. Instead, they should seek a fatwa (religious ruling) from whomever they wish or from whomever they happen to encounter, but without selectively pursuing dispensations. Thus, there is no harm in seeking a fatwa from someone you trust, whether they are Shafi'i, Maliki, or from another school.