We know that God appointed man to be the head of the wife. We also know that God told the wife to submit to her husband. In a Christian marriage this is no problem because they are both to become one in Christ.
Here goes. A non Christian man is married to a Christian woman, and chooses to remain with him. Does this change the Christian woman's responsibility to her husband?
Example, the husband asks her to go fishing on Sunday (Saturday) rather than attend worship services. How should she respond?
I'm not going to let you off the hook with an opinion. Support your position with scripture.
Scripture doesn't shed light on the subject the specific question of does a wife still have responsibility as a Christian wife.
But hear this
1 Corinthians 7:12-15New International Version (NIV)
12 To the rest I say this (I, not the Lord): If any brother has a wife who is not a believer and she is willing to live with him, he must not divorce her. 13 And if a woman has a husband who is not a believer and he is willing to live with her, she must not divorce him. 14 For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband. Otherwise your children would be unclean, but as it is, they are holy.
15 But if the unbeliever leaves, let it be so. The brother or the sister is not bound in such circumstances; God has called us to live in peace.
So if scripture says to stay with the husband inless he wants a divorce then its allowed. And scripture does not say on any page a Christian spouce is not responsible in certain situations. So where the bible is silent, we go with what scripture we have on being a believer as a wife.
Ephesians 5:21-33New International Version (NIV)
Instructions for Christian Households
21 Submit to one another out of reverence for Christ.
22 Wives, submit yourselves to your own husbands as you do to the Lord. 23 For the husband is the head of the wife as Christ is the head of the church, his body, of which he is the Savior. 24 Now as the church submits to Christ, so also wives should submit to their husbands in everything.
25 Husbands, love your wives, just as Christ loved the church and gave himself up for her 26 to make her holy, cleansing[a] her by the washing with water through the word, 27 and to present her to himself as a radiant church, without stain or wrinkle or any other blemish, but holy and blameless. 28 In this same way, husbands ought to love their wives as their own bodies. He who loves his wife loves himself. 29 After all, no one ever hated their own body, but they feed and care for their body, just as Christ does the church— 30 for we are members of his body. 31 “For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.”
32 This is a profound mystery—but I am talking about Christ and the church. 33 However, each one of you also must love his wife as he loves himself, and the wife must respect her husband.
So by the wife obeying her Christian responsibilities could very possibly sanctify her husband by her imitating Christ very well could lead him to Christ.
Luke 14:26New International Version (NIV)
26 “If anyone comes to me and does not hate father and mother, wife and children, brothers and sisters—yes, even their own life—such a person cannot be my disciple.
Her responsibilities as a disciple should come before anyone or anything else.
