Is it obligatory to completely shun a sister who is married to a Christian, and what is the ruling on speaking to her over the phone, and how should one deal with her gifts whose source of money is unlawful, knowing that the mother refuses to shun her and the family benefits from her husband’s money?

The marriage of a Muslim woman to a Christian man is invalid by scholarly consensus, based on the Almighty's saying: "And do not marry polytheistic men until they believe." This marriage is considered unlawful sexual intercourse, and they must be separated immediately. Whoever deems such a marriage permissible, knowing it is forbidden, becomes an apostate disbeliever.

As for shunning her, if there is hope for her guidance, then do not shun her but strive to bring her back to rectitude. If hope is lost, then shunning her is recommended by scholarly consensus, meaning you should not speak to her, connect with her, or eat with her. This is because shunning people who persist in sins is a branch of faith. The prohibition of shunning for more than three days applies to personal matters. However, shunning people of heresies and innovations is permanent unless they repent. One should not greet an innovator or a transgressor.

Regarding the money they accept from her husband, if you are certain it is unlawful money, then give it away in charity. If it is from her lawful money, there is no harm, but it is preferable to return it to her if you despair of her repentance.