Acts 10:34 Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons...
Deut. 10:17 For the LORD your God is God of gods, and Lord of lords, a great God, a mighty, and a terrible, which regardeth not persons, nor taketh reward...
Romans 2:11 For there is no respect of persons with God.
Galatians 2:6 But of these who seemed to be somewhat, (whatsoever they were, it maketh no matter to me: God accepteth no man's person:) for they who seemed to be somewhat in conference added nothing to me... (cf. Eph. 6:9, Col. 3:25, 1 Peter 1:17)
In light of the above verses, critics often ask, "How then could God have chosen the Jews "above all people that are upon the face of the earth"? (Deut. 7:6) Part of the clue is in knowing what it is the Jews were "chosen" for; in that respect, see Glenn Miller's item at the link below. That said, note as well the reasons for God's choice is Deut. 7:8:
But it was because the LORD loved you and kept the oath he swore to your forefathers that he brought you out with a mighty hand and redeemed you from the land of slavery, from the power of Pharaoh king of Egypt.
The reason, then, that the one people were chosen was because of the acts of obedience of their forefathers. Now let's look at one of the other verses:
Acts 10:34-5 Then Peter began to speak: I now realize how true it is that God does not show favoritism but accepts men from every nation who fear him and do what is right.
Note the distinction here: God accepts those who fear him and do what is right - so that acceptance is not the result of favoritism, but of merit in Gods service. Similarly, in the rest of the citations, the point is that men are not accepted or given special privileges based on their own "virtues", but rather, in their attitudes towards God and the resultant behavior.
Further, all of the NT cites use, or use a variation of, the word prosopoleptes, which means "an accepter of face" -- let's see what this means in human terms:
James 2:1-2 My brethren, have not the faith of our Lord Jesus Christ, the Lord of glory, with respect of persons. For if there come unto your assembly a man with a gold ring, in goodly apparel, and there come in also a poor man in vile raiment; And ye have respect to him that weareth the gay clothing, and say unto him, Sit thou here in a good place; and say to the poor, Stand thou there, or sit here under my footstool: Are ye not then partial in yourselves, and are become judges of evil thoughts?
"Respect of persons" has nothing to do with covenantal agreements, or even judgment based on merit, but with judgments based on our own suppositions and deductions. (The Hebrew in Deut. 10:17 for "persons" likewise means "countenance" or "face".) In other words, it means God does not take people at "face value" but searches them out. There is no relevance to the matter of the choice of Jews for service; they were chosen because their forefathers, and they, were obedient.
Objection: This is semantic trickery. That the one people were chosen was because of the acts of obedience of their forefathers, actually is favoritism, plain and simple.
Favoritism defines out as one of two things: "an inclination to favor some person or group" or "unfair treatment of a person or group on the basis of prejudice". Neither of these applies here, since any person was eligible to become a Jew (like Ruth).
Beyond this is the understanding of what "favoritism" means in a social-science perspective in the NT. The core issue is that God does not judge by "face value" -- He doesn't judge a book by its cover.
Wouldn't this meaning of prosopolepsia apply equally well if the choice was not between a man dressed in rich clothes and a man dressed in rags, but between a man of noble birth and a man of common birth? If so, then the contradiction is maintained, because such a standard is exactly the one by which God concluded the Israelites were worthy.
Actually, no, it wasn't. As noted in the article on the Land Promise issue, showing the continued adherence to the covenant was necessary for the Jews to keep occupation of their land.
Where are we ever told that God gave sets of rules to other peoples as well?
Try Romans 1-2.