Bible Questions and Answers

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Thanks for your question.

Please keep the channels of communication open. The Old Testament is full of admonitions against marriage with the unbeliever.  See also 2 Corinthians 6:14-18. 
However, while not relenting in your principles, you must continue to show the love of Christ to your sister's husband and to your sister so that they will listen to you when you encourage him to take on the saving name of our Lord Jesus Christ. Shutting down all communication will not work.  Effective witness requires communication. 
One non-threatening way to help them is to encourage them to take the online Bible Study course on That's something they could do together and they will have access to helpful and knowledgeable Bible tutors who will be happy to answer their questions.
I hope that has been helpful,
God bless!