There is a difference in the Greek spelling of "respect of persons" between the Textus Receptus and the Nestle/Aland 26, but spelling differences do not typically address "meaning".
I. The Statement "There is no respect of persons with God" Needs Careful Thought.
A. Partially because the phrases "to the Jew first, and also to the Greek" of verse 10 and its very near corollary in verse 9, "of the Jew first, and also of the Greek" seem to very deliberately instill in the reader a "respect of persons" [why say "first" and then "also" if there is to be no "respect of persons"?].
B. And partially because Paul takes on the "no respect of persons" concept in verses 11-16 in order to explain himself. There is no reason to "explain" oneself if there are no boundaries to one's meaning.
II. What, Then, Does "No Respect of Persons" Mean?
A. Fundamentally, it means that there will be no unwarranted latitude given to anyone because of issues outside the boundaries already established.
1. "Unwarranted latitude" means that the standards of "judgment" on the Day of the Revelation of the Righteous Judgment of God will not be "adjusted" on the basis of any characteristic the one standing for judgment may have that is outside the standards of "justice".
a. These standards have been given in chiastic fashion in verse 7-10.
b. These standards will not be altered on a case-by-case basis because of any non-related issue.
2. With men, there are often issues that are outside the pale of those already-established as the criteria for decisions.
a. For instance, with men it often makes a great deal of difference "who" a person is when it comes to applying "judgment" to them.
1) The parents of a murderer think quite differently about the nature of the judgment to come upon the murderer than do the parents of the murdered.
2) The citizens of a country often think quite differently about the application of law to an alien than does the alien.
b. Also, it often makes a difference to men "what" a person can do/has done when it comes to applying "judgment" to them.
1) In our legal system, the ability to pay for a defense team often has as much to do with the verdict as the facts of a case.
2) In the sentencing phase, the "judgment" is often mitigated or increased because of what a person has done.
B. Why, then, does Paul deliberately insert the "identity" (who they are) issue into the picture with the terms "Jew" and "Greek".
1. First, because these identities facilitate an easily identifiable difference between "persons".
2. Second, because these identities not only carry "identity" issues with them, but "privilege/lack of privilege" issues with them.
a. The absence of "respect of persons" automatically removes the "identity" issue from consideration.
b. But, the righteousness of the judgment also automatically inserts the issue of "the level of guiltiness".
1) Throughout God's revelation to man, it has been made clear that "guilt" is associated with "level of privilege and knowledge" ("...to whom much is given, much is required..." and "...if you were blind, you would have no sin..." and "...where there is no law, there is no imputation of sin...").
2) In this context, Paul acknowledges certain "privileges" extended to the Jew (see Romans 3:1 in context).
c. Therefore, though no one will be judged on a different basis because of identity issues, all will be judged in respect to the level of privilege extended to them during their lifetime. ["And that servant, which knew his lordís will, and prepared not himself, neither did according to his will, shall be beaten with many stripes. But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes." Luke 12:47-48.]
III. How Does This Doctrine Align With the Biblical Concept of Election?
A. The Bible teaches a doctrine of the "elect" that puts them into a special category of people for whom God acts in a way that He does not act for any outside that category.
B. Is this not "respect of persons"?
1. The foundations of "respect of persons" are rooted in "changing already established rules".
2. The "changing" is linked to the "who" or "what" that is inherent in the "person" to whom "respect" is intended.
3. The doctrine of divine election is almost invariably cast by men into the issue of "respect of persons" with the protest that "election is not fair", but the Bible takes great pains to remove election from justice by making election the display of grace.
4. Since "election" is completely one-sided (the Elector decides who will be elected with no established guidelines), it stands completely outside the definition of "respect of persons".
a. The Bible does not teach anywhere that God will treat all human beings the same.
b. The human attempt to force the idea that no one should ever get anything he doesn't "deserve", or that all should have equal opportunity to obtain a given benefit by their efforts, is nothing more or less than a demand that God deal only in justice.
c. The demand that God only deal in justice is generally only made by those who have an unwarranted perception of their own "righteousness".
IV. How Does This Doctrine Align With the Biblical Concept of Human Incapacity?
A. According to the texts alluded to earlier [see II.B.2.b.1) above], "justice" takes into account the relative levels of human capacity/incapacity.
B. But, according to Luke 12:47-48, even "incapacity" does not eliminate the standards.
1. The text establishes that certain behaviors are "worthy of stripes" even in the face of ignorance (which is a form of incapacity).
2. The text also establishes that any who engage in those behaviors will receive stripes.
3. This means that there is an "ought" that stands without consideration of "capacities/incapacities".
V. How Does This Doctrine Align with the Gospel?
A. It has nothing to do with the Gospel.
B. The Gospel is about Grace; No Respect of Persons is about Law.