N.T. Wright argues that the major failing of the Judaism(s) of Jesus' time was their prideful exclusivity. In his book,
Climax of the Covenant, and elsewhere, Wright argues that a version of ethnic or racial exclusivism resulted in the exclusion of Gentiles from Israel.
While part of the argument seems right, I don't think Wright nails the argument. (I don't either, mind you. I'm just noting why I don't so far find Wright's argument convincing.)
First, the part that is right: Jesus' public ministry begins in Luke with preaching that God's grace extends to Gentiles (Lk 4.25-27). In response, those listening to him in the synagogue seek to kill him (vv. 28-29). This certainly dovetails with OT themes such as those found in Jonah, where Jonah bitterly laments the grace that God shows to Nineveh. Since the promise to Abraham is that, through him, God will bless the Gentiles -- a promise that Paul identifies as the Gospel (Gal 3.8) -- then opposition to doing this is an attack on the very purpose for which God called Israel into existence. So this attitude can't be a good thing for Israel's relationship with God.
That being said, it seems to me that there must be something more at work here than ethnic exclusivism. After all, Jesus himself reports that the scribes and Pharisees were zealous for Gentile converts:
Woe to you, scribes and Pharisees, hypocrites, because you travel about on sea and land to make one proselyte; and when he becomes one, you make him twice as much a son of hell as yourselves (Mt 23.15).
Similarly, from the beginning, those who were circumcised included people not physically related to Abraham (Gn 17.12, 23). Indeed, the large majority of those circumcised were not physically related to Abraham (Gn 14.14). Foreigners would become as a "native of the land," receiving all privileges thereof, via circumcision (Ex 12.48).
Membership in Israel was therefore not a closed classification. The Jews with whom Jesus repeatedly clashed were in fact zealous for converts.
Further, while I imagine that circumcision is more painful than baptism, there is nothing in principle in circumcision that prevented Israel from thinking of their mission to be to "Go forth and circumcise all nations, teaching them to observe all that Yahweh commanded you." Israel could bring Gentiles into God's kingdom via circumcision, much the same as the church brings nonbelievers into God's kingdom via baptism.
So given that the category of "Israel" was in fact an open classification in which non-Israelites could become Israelites via circumcision, and given that the scribes and Pharisees of Jesus' day
wanted to turn non-Israelites into Israelites, I don't see that ethnic "exclusivism" on the part of Israelites can be the specific problem that Jesus and Paul contrast with the Gospel. It has to be something else.
I won't hazard a guess now regarding what that something else is. But I remain unconvinced that Wright's answer is the correct one.