Disclaimer: This article will have controversial views and religious bias.
Should Christians date non-Christians? This is a really controversial question and you will get different answers from everyone that you ask. This article will just convey my opinions and views on the topic. That being said, there is a biblical passage that indirectly addresses the question at hand.
Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness? - 2 Corinthians 6:14
What this passage is basically saying is that Christians shouldn't have relationships with non-believers, including friendships, if I'm not mistaken. Now this is an extremely outdated and extreme stance on this topic, and I don't quite agree with the verse. All I am going to say is that it is probably not in our best interests to be romantically involved with a non-believer, but not because the Bible says so.
Is it a sin?
Some people might go so far as to say that dating a non-Christian would be a sin. But it would be in very technical terms. The argument would be that by dating a non-believer we are technically not trusting in the Lord and not waiting for his best for us (which would be a Christian). Therefore, we are saying that we choose someone else over the love and plans that Christ has lain out for us, which therefore would be a sin. In my opinion, it is a bit of a stretch to call it sin and I hold my view because of different reasons, mainly compatibility issues.
They do not share the same core beliefs.
As believers, we can pretty much say that our religion is not only a belief but it is a lifestyle. If we plan on dating someone who won't tolerate or understand our different styles of life, then conflict may arise. Believing in God and loving him is fundamentally who we are as people and it would be really hard for someone to understand that if they aren't believers as well. If we do choose to have a relationship with them, we are almost forced not to give them all of us or most of us. We can only share with them part of us.
Our views on marriage are different.
Christians hold marriage up to a much higher level of intensity than the conventional view on marriage right now. Marriage in Christianity is basically a reflection of how much Christ loves the church. It is a promise of unconditional love, a promise such as Christ made when he died on the cross for us. Marriage is not just to announce a lifelong relationship but it is also saying that we will try to be more like Jesus through it. A non-Christian would not only not understand our views on marriage but will also be anchoring their marriage on their love for their partner. Of course, it isn't wrong to do so, but like almost everything else, love can break even though it can be very strong. It's much better to anchor your marriage in God because God is the only thing that's perfect and everlasting, and you can't anchor your marriage in God unless both partners believe in him.
Efforts to grow closer to a partner will take us farther from Christ.
If we do choose to have a relationship with a non-believer, we will be growing further and further away from Christ as we try and grow closer to our partner. The inverse will happen if we try to grow closer to Christ. Since this is the case, then our relationship with Christ should always be the priority. The solution to this was mentioned in my last article, which talks about the triangle of dating, but basically the relationship with our partners will be strengthened as a byproduct of both partners pursuing a stronger relationship with God.
Again, these are just my thoughts and opinions, and are in no way backed up by the Bible specifically.