10 “When you go out to war against your enemies, and the Lord your God gives them into your hand and you take them captive, 11 and you see among the captives a beautiful woman, and you desire to take her to be your wife, 12 and you bring her home to your house, she shall shave her head and pare her nails. 13 And she shall take off the clothes in which she was captured and shall remain in your house and lament her father and her mother for a full month. After that you may go in to her and be her husband, and she shall be your wife(Deut. 21:10-13)
This text is about as straightforward an affirmation of the propriety of interracial marriage, provided certain conditions are operative, as they come. The only condition that obtained was that the woman renounce her affiliation with and allegiance to the religion of the nation from which she had come. This is precisely how Calvin understands the text:
As regarded the Canaanites, who were destined and devoted to destruction, we have seen that the Israelites were prohibited from taking their women to wife, lest this connection should be an enticement to sin; but Moses now goes further, viz., that the Israelites, having obtained a victory over other nations, should not marry any of the captive women, unless purified by a solemn rite...But since many are led astray by the blandishments of their wives, God applies a remedy, viz., that the abjuration of their former life should precede their marriage; and that none should be allowed to marry a foreign wife until she shall have first renounced her own nation. To this refers the ceremony, that the woman should shave her head, and cut her nails, and change her garments, and lament her father and her family for an entire month, viz., that she may renounce her former life, and pass over to another people...I have no doubt but that their month of mourning, their shaven head, and the other signs, are intended by God for their renewal, so that they may accustom themselves to different habits. And with the same object they are commanded to bewail their parents as if dead, that they may bid farewell to their own people. To this the Prophet seems to allude in Psalm 45:10, when he says, "Hearken, O daughter, and consider, and incline thine ear; forget also thine own people, and thy father's house;" for he intimates that otherwise the marriage of a foreign woman with Solomon would not be pure and legitimate, unless she should relinquish her superstitions, and devote herself to God's service. Nor was it needless that God should require the Israelites diligently to beware lest they should take wives as yet aliens from the study of true religion, since experience most abundantly shows how fatal a snare it is. But although we are not now bound to this observance, yet the rule still holds good that men should not rashly ally themselves with women still devoted to wicked superstitions(Calvin on Deut. 21:10-13).
Note first that Calvin points out that the Israelites were prohibited from marrying the Canaanites, whom God had devoted to destruction. But women from the other nations are allowed to marry the Israelite men provided they undergo the proper rituals involving disavowal of their former way of life, and conversion to Judaism. Calvin uses Solomon's marriage to Pharaoh's daughter(cf. 1 Kgs. 3:1) as an example of this, and understands Ps. 45:10 as speaking of this very event:
I have no doubt, that what is here said is spoken of the Egyptian woman, whom the prophet has described as standing at the right hand of the king. It was not, indeed, lawful for Solomon to marry a strange woman; but this of itself is to be accounted among the gifts of God, that a king so powerful as the king of Egypt was,  sought his alliance. At the same time, as by the appointment of the Law, it was required that the Jews, previous to entering into the marriage relation, should endeavor to instruct their wives in the pure worship of God, and emancipate them from superstition; in the present instance, in which the wife spoken of was descended from a heathen nation, and who, by her present marriage, was included in the body of the Church, the prophet, in order to withdraw her from her evil training, exhorts her to forget her own country and her father's house, and to assume a new character and other manners. If she did not do this, there was reason to fear, not only that she would continue to observe in private the superstitions and false modes of worshipping God to which she had been habituated, but that also, by her public example, she would draw away many into a similar evil course; and, indeed, this actually came to pass soon after. Such is the reason of the exhortation which the prophet here gives her, in which, in order to render his discourse of more weight, he addresses her by the appellation of daughter, a term which it would have been unsuitable for any private man to have used. The more clearly to show how much it behoved the new bride to become altogether a new woman, he employs several terms thereby to secure her attention, Hearken, consider, and incline thy ear It is certainly a case in which much vehemence and urgent persuasion are needed, when it is intended to lead us to a complete renunciation of those things in which we take delight, either by nature or by custom. He then shows that there is no reason why the daughter of Pharaoh should feel any regret in forsaking her father, her kinsfolk, and the land of Egypt, because she would receive a glorious recompense, which ought to allay the grief she might experience in being separated from them. To reconcile her to the thought of leaving her own country, he encourages her by the consideration that she is married to so illustrious a king.
Calvin makes an obvious reference to Deut. 21:10-13 in his commentary on this very scripture, when he notes that the Law allowed marriage to non-Israelites provided they renounced the religious customs of their previous nations and converted to Judaism.
There are certainly some women whom the Israelites were unconditionally forbidden to marry, however:
10 “When you draw near to a city to fight against it, offer terms of peace to it. 11 And if it responds to you peaceably and it opens to you, then all the people who are found in it shall do forced labour for you and shall serve you. 12 But if it makes no peace with you, but makes war against you, then you shall besiege it. 13 And when the Lord your God gives it into your hand, you shall put all its males to the sword, 14 but the women and the little ones, the livestock, and everything else in the city, all its spoil, you shall take as plunder for yourselves. And you shall enjoy the spoil of your enemies, which the Lord your God has given you. 15 Thus you shall do to all the cities that are very far from you, which are not cities of the nations here. 16 But in the cities of these peoples that the Lord your God is giving you for an inheritance, you shall save alive nothing that breathes, 17 but you shall devote them to complete destruction,[a] the Hittites and the Amorites, the Canaanites and the Perizzites, the Hivites and the Jebusites, as the Lord your God has commanded, 18 that they may not teach you to do according to all their abominable practices that they have done for their gods, and so you sin against the Lord your God(Deut. 20:10-18).
Recall that Calvin has already noted this in the commentary we have referenced. Note that v. 14 allows the men to marry women from any nation they conquer, but v. 16 qualifies this and forbids the Israelites from marrying the Hittites, Amorites, Canaanites, Perizzites, Hivites or the Jebusites, on the ground that they are devoted to destruction and their land is given to the Israelites as an inheritance. Note also that even in this case, the rationale is not racial at all, but as v. 18 explicitly points out, has specifically to do also with those nations causing Israel to sin in following the practices of their gods. Now let's look at Ezra, a text frequently appealed to by Kinists:
"After these things had been done, the officials approached me and said, “The people of Israel and the priests and the Levites have not separated themselves from the peoples of the lands with their abominations, from the Canaanites, the Hittites, the Perizzites, the Jebusites, the Ammonites, the Moabites, the Egyptians, and the Amorites"(Ezra 9:1).
Does this list look familiar? It should! Israel is explicitly forbidden from marrying everyone on this list in Deut. 20:10-18 on the ground that God is giving their land to Israel as an inheritance, and on the ground that their gods cause Israel to sin. The Ammonites and the Moabites, while not explicitly on the list, are explicitly forbidden from joining the assembly in the Law on other grounds:
“No Ammonite or Moabite may enter the assembly of the Lord. Even to the tenth generation, none of them may enter the assembly of the Lord for ever, 4 because they did not meet you with bread and with water on the way, when you came out of Egypt, and because they hired against you Balaam the son of Beor from Pethor of Mesopotamia, to curse you"(Deut. 23:3-5).
So also Nehemiah:
"On that day they read from the Book of Moses in the hearing of the people. And in it was found written that no Ammonite or Moabite should ever enter the assembly of God, 2 for they did not meet the people of Israel with bread and water, but hired Balaam against them to curse them—yet our God turned the curse into a blessing"(Neh. 13:1-2).
Finally, Solomon is explicitly mentioned as a prime example of an otherwise good king whose heathen wives led him astray, of whom Pharaoh's daughter(1 Kgs. 3:1) is the archetypal example, and as far as I can tell, the only one of Solomon's wives singled out:
"Did not Solomon king of Israel sin on account of such women? Among the many nations there was no king like him, and he was beloved by his God, and God made him king over all Israel. Nevertheless, foreign women made even him to sin"(Neh. 13:26).
Apart from the fact that the reason given for condemning marriage to such "foreign" wives presupposes their rejection of Judaism in noting that these women caused the Israelites to serve other gods and practice the religious customs of their nation, the vast majority of these prohibitions have rather to do with decrees of God related to His promise to the Israelites that Canaan would be their inheritance. Deut. 20:10-18 forbids marriage with these particular nations precisely for this reason. Deut. 23:3-5 likewise prohibits Moabites and Ammonites from even entering the assembly of God. Deut. 21:10-14, meanwhile, explicitly allows the Jews to marry women from other nations provided they convert to Judaism. The relevant prohibitions have nothing to do with miscegenation whatsoever. A similar logic is operative in Gen. 24:3-4. Abraham did not want a wife for Isaac among the Canaanites. God had already told Abraham that the Canaanites were devoted to destruction(Gen. 15:12-21). vv. 17-21 explicitly includes the Hittites among this group, and it should therefore come as no surprise that Esau's marriage to a Hittite had harmful consequences(Gen. 26:34-35).