I've been told that this is called "missionary dating". I believe that it is okay to date this way, but they shouldn't leave you lost in your faith. Dating Christians can be just as hard as dating non-Christians, because we all fall short of His glory at some point, and we are expected to meet their standards or expectations. It all depends on how responsible you are with your faith.
If this is ok where is the biblical precedent?
What if you marry? Are you really content with living your life knowing the person you love and are committed to could end up in hell at any time?
How do you tell your children that their father is going to hell?
How does the non-Christian husband perform his biblical duties as spiritual leader of the household?
How can you raise your children as Christians if they know that you married someone who is not, and there is that division there?
How does a Christian husband be the spiritual leader of a household when his spouse does not follow his lead?
How would you feel if you invested time and emotions into someone, only to realize their intention in the relationship was the convert you to their religion?
How can you justify that sort of emotional manipulation as a Christian?
What if they claim to convert for Your sake? Are they truly repentant? Seeking God? Changed and born again? Or are they following the motions to make you happy?
Or what if you plan on not marrying them?
So then you actively seek out to date someone with only the intention of changing them into what you want. And if they don't become what you want then you hurt them by breaking up with them?
How will this reflect on their view of God to know that you attempted to change and manipulate them in a false relationship setting?
How long will you allow them to be deceived by your actions? Months? Years? Before you break their heart in the name of winning souls for God.
How can you be sure they will not have any negative effects on you or your faith?
How can you justify going against the bibles statement of not being unequally yoked?
Fact is missionary dating is selfish and manipulative. If you were truly concerned about their soul then you would focus on that and not being in a relationship with them.