Is it permissible for a married Muslim man to marry a second wife who consents to it, while her guardian disapproves due to the husband's affiliation with a different madhhab, despite the husband being well-known for his righteousness, and is the guardian's permission obligatory in this case?

The fundamental principle is to marry a suitor who possesses good character and religious commitment, based on the Prophet's (peace be upon him) saying: "If there comes to you one whose religious commitment and character you approve of, then marry [your daughter] to him; otherwise, there will be tribulation on earth and widespread corruption." The guardian should be persuaded that a difference in madhhab (school of thought) does not have an impact. If persuasion is successful, then that is what is sought. Otherwise, obedience to the father is obligatory, unless he withholds her [from marriage unjustly], in which case she may resort to the judge. This is provided that the disagreement is not concerning the fundamentals of religion; if it is, then it is not permissible for the man to marry her.