The most prevalent and often cited passage concerning this is quoted from the second letter of Paul to the Corinthians:
All Scripture is quoted from the King James translation.
2nd Corinthians 6:14 through 18 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
And what concord hath Christ with Belial? or what part hath he that believeth with an infidel? And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people. Wherefore come out from among them, and be ye separate, saith the Lord, and touch not the unclean thing; and I will receive you, And will be a Father unto you, and ye shall be my sons and daughters, saith the Lord Almighty.
Below I have quoted all of the Scriptures that I know of which address interfaith or inter-culture marriage.
Even though this is concerns Abraham finding Rachael for Isaac, and the next scripture concerns Isaac sending Jacob to Laban to find a wife for himself, we find that very early there is a plan to keep the line to Jesus pure and preserve it to the exclusion those other than God's chosen ones.
Genesis 24:3-4 And I will make thee swear by the Lord, the God of heaven, and the God of the earth, that thou shalt not take a wife unto my son of the daughters of the Canaanites, among whom I dwell: But thou shalt go unto my country, and to my kindred, and take a wife unto my son Isaac.
Genesis 28:1-2 And Isaac called Jacob, and blessed him, and charged him, and said unto him, Thou shalt not take a wife of the daughters of Canaan. Arise, go to Padanaram, to the house of Bethuel thy mother's father; and take thee a wife from thence of the daughters of Laban thy mother's brother.
What we find happening after God brings the Nation of Israel out of bondage in Egypt, Is that God directs the Nation of Israel to remain pure from the influence of other Religions, which would denigrate their loyalty to God.
Exodus 34:11-16 Observe thou that which I command thee this day: behold, I drive out before thee the Amorite, and the Canaanite, and the Hittite, and the Perizzite, and the Hivite, and the Jebusite. Take heed to thyself, lest thou make a covenant with the inhabitants of the land whither thou goest, lest it be for a snare in the midst of thee: But ye shall destroy their altars, break their images, and cut down their groves: For thou shalt worship no other god: for the Lord, whose name [is] Jealous, [is] a jealous God: Lest thou make a covenant with the inhabitants of the land, and they go a whoring after their gods, and do sacrifice unto their gods, and [one] call thee, and thou eat of his sacrifice; And thou take of their daughters unto thy sons, and their daughters go a whoring after their gods, and make thy sons go a whoring after their gods.
In the Book of Numbers we see how deviation from that command erodes the dedication to God.
Numbers 25:1-2 And Israel abode in Shittim, and the people began to commit whoredom with the daughters of Moab. And they called the people unto the sacrifices of their gods: and the people did eat, and bowed down to their gods.
Then again in the book of Deuteronomy. We find that God warns the nation of Israel again against intermarrying but here God adds a penalty.
Deuteronomy 7:1-4 When the Lord thy God shall bring thee into the land whither thou goest to possess it, and hath cast out many nations before thee, the Hittites, and the Girgashites, and the Amorites, and the Canaanites, and the Perizzites, and the Hivites, and the Jebusites, seven nations greater and mightier than thou; And when the Lord thy God shall deliver them before thee; thou shalt smite them, [and] utterly destroy them; thou shalt make no covenant with them, nor shew mercy unto them: Neither shalt thou make marriages with them; thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son. For they will turn away thy son from following me, that they may serve other gods: so will the anger of the Lord be kindled against you, and destroy thee suddenly.
In first Kings we find that Solomon carries this to extremes and we find that exactly what God warned against has happened.
1st. Kings 11:2-4 Of the nations [concerning] which the Lord said unto the children of Israel, Ye shall not go in to them, neither shall they come in unto you: [for] surely they will turn away your heart after their gods: Solomon clave unto these in love. And he had seven hundred wives, princesses, and three hundred concubines: and his wives turned away his heart. For it came to pass, when Solomon was old, [that] his wives turned away his heart after other gods: and his heart was not perfect with the Lord his God, as [was] the heart of David his father.
And in the book of Ezra we see that God does exactly what he said he would do in that his anger was turned toward the nation of Israel.
Ezra 9:1-12 Now when these things were done, the princes came to me, saying, The people of Israel, and the priests, and the Levites, have not separated themselves from the people of the lands, [doing] according to their abominations, [even] of the Canaanites, the Hittites, the Perizzites, the Jebusites, the Ammonites, the Moabites, the Egyptians, and the Amorites. For they have taken of their daughters for themselves, and for their sons: so that the holy seed have mingled themselves with the people of [those] lands: yea, the hand of the princes and rulers hath been chief in this trespass. And when I heard this thing, I rent my garment and my mantle, and plucked off the hair of my head and of my beard, and sat down astonied. Then were assembled unto me every one that trembled at the words of the God of Israel, because of the transgression of those that had been carried away; and I sat astonied until the evening sacrifice. And at the evening sacrifice I arose up from my heaviness; and having rent my garment and my mantle, I fell upon my knees, and spread out my hands unto the Lord my God, And said, O my God, I am ashamed and blush to lift up my face to thee, my God: for our iniquities are increased over [our] head, and our trespass is grown up unto the heavens. Since the days of our fathers [have] we [been] in a great trespass unto this day; and for our iniquities have we, our kings, [and] our priests, been delivered into the hand of the kings of the lands, to the sword, to captivity, and to a spoil, and to confusion of face, as [it is] this day. And now for a little space grace hath been [shewed] from the Lord our God, to leave us a remnant to escape, and to give us a nail in his holy place, that our God may lighten our eyes, and give us a little reviving in our bondage. For we [were] bondmen; yet our God hath not forsaken us in our bondage, but hath extended mercy unto us in the sight of the kings of Persia, to give us a reviving, to set up the house of our God, and to repair the desolations thereof, and to give us a wall in Judah and in Jerusalem. And now, O our God, what shall we say after this? for we have forsaken thy commandments, Which thou hast commanded by thy servants the prophets, saying, The land, unto which ye go to possess it, is an unclean land with the filthiness of the people of the lands, with their abominations, which have filled it from one end to another with their uncleanness. Now therefore give not your daughters unto their sons, neither take their daughters unto your sons, nor seek their peace or their wealth for ever: that ye may be strong, and eat the good of the land, and leave [it] for an inheritance to your children for ever.
And in the book of Nehemiah. We find that just as God has warned, the children of these marriages not only have strayed from the worship of God, but they have also strayed from the language of Israel.
Nehemiah 13:23-30 In those days also saw I Jews [that] had married wives of Ashdod, of Ammon, [and] of Moab: And their children spake half in the speech of Ashdod, and could not speak in the Jews' language, but according to the language of each people. And I contended with them, and cursed them, and smote certain of them, and plucked off their hair, and made them swear by God, [saying], Ye shall not give your daughters unto their sons, nor take their daughters unto your sons, or for yourselves. Did not Solomon king of Israel sin by these things? yet among many nations was there no king like him, who was beloved of his God, and God made him king over all Israel: nevertheless even him did outlandish women cause to sin. Shall we then hearken unto you to do all this great evil, to transgress against our God in marrying strange wives? And [one] of the sons of Joiada, the son of Eliashib the high priest, [was] son in law to Sanballat the Horonite: therefore I chased him from me. Remember them, O my God, because they have defiled the priesthood, and the covenant of the priesthood, and of the Levites. Thus cleansed I them from all strangers, and appointed the wards of the priests and the Levites, every one in his business;
In Matthew Jesus warned that we cannot serve two masters. And even though in this case he was talking about money, or wealth, the same would apply to gods.
Matthew 6:24 No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
Luke 16:13 No servant can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
God is a jealous God and obviously his reason for these restrictions is that he does not want the worship of himself diluted by worship to any other god's.
Exo 20:1 through 3 And God spake all these words, saying, I am the LORD thy God, which have brought thee out of the land of Egypt, out of the house of bondage. Thou shalt have no other gods before me.
As far as Christianity is concerned this would appear to be the reason God has set all of these restrictions into place as far as Christian belief goes.