In the Old Testament, God has issued many warnings to the people of Israel not to marry people of different nations. If you look at the reason why this is so, it is not because they are of a different race but because of their idolatrous practice. They do not share the same spiritual faith.
12 Be careful not to make a treaty with those who live in the land where you are going, or they will be a snare among you.
13 Break down their altars, smash their sacred stones and cut down their Asherah poles.
14 Do not worship any other god, for the LORD, whose name is Jealous, is a jealous God.
15 "Be careful not to make a treaty with those who live in the land; for when they prostitute themselves to their gods and sacrifice to them, they will invite you and you will eat their sacrifices.
16 And when you choose some of their daughters as wives for your sons and those daughters prostitute themselves to their gods, they will lead your sons to do the same.
Why did God issue this command? I've found the answer in another bible reference:
12 Else if ye do in any wise go back, and cleave unto the remnant of these nations, even these that remain among you, and shall make marriages with them, and go in unto them, and they to you:
13 Know for a certainty that the Lord your God will no more drive out any of these nations from before you; but they shall be snares and traps unto you, and scourges in your sides, and thorns in your eyes, until ye perish from off this good land which the Lord your God hath given you.
God has given us promises in our lives. When we walk out of His perfect will and marry an unbeliever, we are exposing ourselves to thorns and snares that will hinder our spiritual progress and us possessing the promises that God has set for us in our lives.
The spirit of this is carried again and reclarified into the New Testament:
[2 Cor 6:14]
Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
In my personal opinion, it is not wrong to date someone of another race ... the issue is whether the person's spiritual state: a believer or an unbeliever.