Acts 10:34-5 Then Peter began to speak: ?gI 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.?h
Note the distinction here: God accepts those who ?gfear him and do what is right?h - so that acceptance is not the result of favoritism, but of merit in God?fs 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.