Must a vow, whose underlying reasons were undertaken out of ignorance that they were a Bid'ah (innovation in religious matters), be fulfilled after it becomes clear that they are indeed a Bid'ah?

If the vow aims at refraining from an innovation (bid'ah), then it is considered a vow of lajaj (obstinacy) and anger. If the vowed act is a sin, then it is forbidden to fulfill it, based on the Prophet's (peace and blessings be upon him) saying: "There is no fulfillment in disobedience to Allah," and "Whoever vows to disobey Allah, let him not disobey Him." However, if it is an act of obedience or permissible, the vower is given the choice between fulfilling it or offering an expiation (kaffarah) for an oath. If it is disliked (makruh), then expiation is recommended, and the act should not be done; but if it is done, there is no expiation.