So there is a theme of being out in the world but not of it. I'm not aware dating is addressed directly and we can define it many ways from casual to with benefits. If you read the Old Testament you will see the repeating story of intermarrying leading to idolatry.
That would include business partnerships as well as personal. Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? What harmony is there between Christ and Belial? Or what does a believer have in common with an unbeliever. What agreement is there between the temple of God and idols?
For we are the temple of the living God. There is a reality that while not forbidden it is unwise. A non-Christian will never understand and frequently not accept this. Statistically bad will come of it and you will compromise your priority. That said, it does happen often enough that the non-Christian partner is converted. Casual friendships and dating would not be a problem unless it distracts you from your beliefs and calling.
As with the other persons answers the best and most direct text is 1 Corinthians 7: Otherwise, your children would be unclean, but as it is they are holy. For God has called usl to peace. As a Catholic I will add the Church's view on what it calls the "disparity of cult: It requires particular attention on the part of couples and their pastors.
A case of marriage with disparity of cult between a Catholic and a non-baptized person requires even greater circumspection. But the difficulties of mixed marriages must not be underestimated. They arise from the fact that the separation of Christians has not yet been overcome. The spouses risk experiencing the tragedy of Christian disunity even in the heart of their own home. Disparity of cult can further aggravate these difficulties. Differences about faith and the very notion of marriage, but also different religious mentalities, can become sources of tension in marriage, especially as regards the education of children.
The temptation to religious indifference can then arise. Its task is to help such couples live out their particular situation in the light of faith, overcome the tensions between the couple's obligations to each other and towards their ecclesial communities, and encourage the flowering of what is common to them in faith and respect for what separates them.
But beware, the enemy is a matchmaker too. He will never lead you astray. Is it right for a Christian to date or marry a non-Christian? Don't Take It from Me: What does the Bible say about believers dating unbelievers? Why Dating Outside the Faith is Illogical http: