Question:
Should you date someone that isn’t saved, because you think you can change them?

Answer:
There are a number of definitions to the word “date,” but I believe that dating is when two people are interested in each other and are corresponding frequently or getting together a lot in order to get to know each other better with the idea always in mind that they might someday get married.

The Bible speaks of marriage as the only romantic long-term relationship between a man and a woman. It does not speak of a man and woman living together and having a physical relationship outside of marriage. Therefore, all romantic relationships should have marriage as a goal.
Second Corinthians 6:14 says to not be unequally yoked together with unbelievers. Marriage is definitely a binding yoke. Dating would not be a binding yoke in the same way, but there is a yoke there because there is always pain involved when the dating yoke is broken and the two people break up.
I don’t think that it is a wise thing to get into a dating relationship with an unsaved person with marriage being the goal ahead of you. Once the emotions get involved, it is a very difficult thing to break the relationship because your partner is not saved. I believe that it is better to not get into it in the first place, but instead encourage someone of the same sex as that person to help them spiritually.
Another reason for staying away from a dating relationship with an unsaved person is that your primary goal will be to change that person or try to convince them of their need for salvation. A healthy relationship is based on acceptance of another person, not on trying to change them. If that person would get saved while you are dating them, it may be difficult to ever know whether they just said some words in order to make you think they got saved or whether they truly did get saved.
The same holds true for someone who is not in fellowship with you. They could desire to be in fellowship with the assembly in order to please you, instead of having the truth revealed to them of the one body of Christ and our responsibility to express our membership in that body.These thoughts are not hard and fast rules, because the Lord has blessed people who have entered dating relationships with unsaved people, and then the person got saved and are happily married now. It may save a lot of heartache though, to wait until the Lord brings someone into your life who loves the Lord and desires to walk with Him.