If I may be so bold, Wright's ideas of justification, are not only not Reformed, they're not Lutheran, nor even within the scope of Protestant Christianity!!
During the Reformation a sharp distinction was made between Protestants and non-Protestants concerning the doctrine of justification by faith alone (in Christ alone) which is by grace alone. The Solas are Protestant doctrines which binds all Protestants together. Mr. Wright seems to have lost sight of the fact that the doctrine of justification by faith alone was one of the chief reasons behind the Reformation.
He actually teaches justification by faith alone.
I just refreshed my memory on Wright's book on justification. I believe his position is consistent with both Paul and Calvin. Whether he is consistent with the later Reformed tradition I'm not in a position to judge.
In the chapter on justification, Calvin appears to say, with Paul, that when God wanted to save us, he sent Jesus to die for us, and united us with Christ. Faith is the way we participate in that union. Justification then follows from faith. It is one of two results of being in Christ, the other being sanctification. I believe this is the usual understanding of Calvin's "ordo salutis." It's certainly the one McGrath describes.
I don't always agree with every detail of Wright's presentation, but this is his basic scheme. His concern is that justification has, for many Protestants, come to be God's entire way of reconciling us to himself. In fact, justification is a result of the cross, and what Paul calls being in Christ, and Calvin calls the "unio mystica," through faith. That's why faith is reckoned as righteousness, an act that he also called justification.
Wright says "for Paul, "justification" was something that happened "in the Messiah." The status the Christian possesses is possessed because of that belongingness, that incorporation. This is the great Pauline truth to which the sub-Pauline idea of "the imputation of Christ's righteousness" is truly pointing." Quite so. At least in the institute, I have been unable to find Calvin saying that Christ's righteousness is imputed to us. Rather, Paul at least says our faith is imputed as righteousness. That is, justification is God's recognition (and in some cases, God's performative declaration) that we are in the right because we God has put us in Christ.
This is not infused righteousness either. Our Christian life develops over a whole lifetime. Justification does not recognize that we've achieved anything. It recognizes that we are in Christ, and as his person, Christ will over time change us.
Paul, however, tends to use language in fairly particular way: Paul says that by being united with Christ we have already died to sin and risen to new life. This is not a statement about our accomplishments. It is a statement that our ownership has changed. We're now God's servants, not servants of sin. We are living a new life, even if it's not yet very visible. Paul says we're already new people; now we have to live up to it. He does not say we are Christians only to the extent we obey, but that we are already Christ's, but need to show that in our lives.
It is this change in ownership that justification represents.
While neither Calvin or Wright say exactly the same thing I have here, I think both see justification as a declaration that we are Christ's, not by an absolute exercise of God's authority, but on the grounds of his already having united us with Christ and made us his. Thus our faith is reckoned as righteousness, because faith is our participation in this union.
Note that Wright does not object to justification by faith. He agrees with that. What he objects to is justification by imputation of Christ's righteousness, an idea that is present neither in Paul nor Calvin.
I fear that Wright is more an expert in the 1st Cent than the 16th, and that he may be criticizing something that isn't actually Calvin's views. But I think we should judge him as Reformed by how well he understands the Bible, not how well he understands Calvin.
It is also unfortunate that Wright (at least in this book) appears to deny imputed righteousness. What he actually denies is that Christ's righteousness is imputed to us. But that's not what Paul (or Calvin, as far as I can see) says. Paul says that faith is imputed as righteousness. That's what justification by faith is. I believe Wright accepts that. So I believe Wright teaches imputed righteousness, even though he appears to reject it.