Should one continue receiving Quran lessons and memorizing it from a female teacher who permits uncovering the face and hands in front of non-mahram men, claims that the niqab has no basis in religion, and forbids following the fatwas of Saudi scholars?

There is no harm in continuing to learn the Quran and knowledge with the teacher, even if you hear from her statements that differ [from your views], for many issues, including the issue of niqab, are matters of ijtihad (independent reasoning) in which it is not permissible to condemn those who differ or to be fanatical about one's opinion. It is necessary to understand the fiqh of differing opinions, for in matters of ijtihad where there is no definitive proof, it is permissible to adopt either of the two opinions, and it is not permissible to condemn someone who adopts the other. The teacher who disparages the opinion of the obligation to cover the face and considers it an extremism, she herself falls into extremism by trying to compel people to her opinion. As a muqallidah (follower of a madhhab), she has no right to condemn other muqallids, nor to disparage the opinions of the mujtahid scholars. It is permissible for a Muslim to follow someone whose knowledge and piety they trust, and it is not permissible to force others to follow a specific scholar. Some Maliki jurists consider the entire woman to be awrah. It is advisable to stay away from argumentation and extremism, and to benefit from their efforts in teaching the Quran, and to leave aside what causes discord.