What is the most appropriate action to take towards a female relative who married a Christian man despite her family's disapproval, and should relations with her be severed, as one shaykh has decreed, or not?

The ruling on boycotting depends on what serves the best interest. If boycotting helps bring the woman back to the truth, then it is preferable. However, if maintaining ties while continuously advising her is more beneficial, then maintaining ties is preferable. The marriage of a Muslim woman to a non-Muslim is null and void, without any difference of opinion, based on the Almighty's saying: {And do not marry [your daughters] to idolaters until they believe} (Quran 2:221). It is obligatory upon the woman's family and everyone who knows of her marriage to a Christian to strive to separate them by all lawful means, including bringing the matter before a Sharia judge. They are not permitted to merely boycott her and remain silent about this evil; rather, they must take immediate action due to the impermissibility of this relationship's continuation and perpetuation.