Unbelieving family members
My sisters and I were raised by our Catholic mother and our father, now deceased, who was a non-practicing Baptist. As adults, my sisters and I have taken far different paths in our faith life. The oldest sister is estranged from our mother and I consider her to be an atheist. The middle sister seems to mix some elements of Catholicism with astrology. I, by God's grace, am a member of the WELS. My oldest sister and I have had a limited relationship for many years. Recently, we've been working on building our relationship. She knows that my faith is in Christ Jesus and clearly doesn’t want to hear about, yet seems to respect my choices. Understanding the need to be both a Christian example to her and guard my faith, when is it unacceptable to be "yoked together"? (2 Corinthians 6:14-15).
Your concern for upholding biblical principles is commendable. So is your desire to befriend your sister and provide her with a Christian example.
The Scripture passage you cited is in the context of taking part in idolatrous worship with others and joining together with false teachers. That does not sound like your situation at all. I understand you wanting to re-establish and strengthen ties with a sibling—being a Christian example to her so that she can be influenced positively by your faith (Matthew 5:16). Friendship with unbelievers becomes problematic when they influence Christians negatively.
By all means continue to show your sister what Christ and Christianity are all about. God bless you and your efforts.