I am not sure whether this is a doctrinal topic, but this seemed the most suitable domain for it.
I also apologize to any who are utterly unfamiliar with what has been dubbed the "New Perspective". I simply cannot give a full description of it here; but hopeful a discussion will fill in the blanks.
The New Perspective challenges the Old Perspective on Paul. The Old Perspective (traced primarily back to Luther) saw the decisive difference between Christianity and Judaism as that between Grace and Works (or faith and Law). Judaism was a "works-righteous" religion, in which one had to accrue sufficient merit to obtain admission to heaven; Christianity declared that no amount of merit was sufficient, and yet, via Jesus, we can obtain admission all the same.
The New Perspective looks at Jewish texts of the period "on their own terms". It finds that ancient Judaism knew all about Grace and faith. The "laws" which needed to follow were a result of salvation (in their case the Exodus---God saved them first from Egypt, and only then gave them the laws). There are numerous prayers not only from the New Testament but from non-canonical texts demonstrating that Grace was no foreign concept to Jews before Christ....
...the question arises, if the problem with Judaism was not its "works-righteous" bent, then what was the problem with Judaism? And what are we to make of those passages which seem to condemn Judaism as a "works-righteousness" religion?
Some theories have been put forward by scholars:
1) there was no problem; Paul didn't understand his own religion.
2) the problem was that Judaism was exclusive; it didn't include Gentiles
3) the problem was that the Law could not produce righteousness.
Of course, this topic is very broad: it can lead to an outright rejection of the New Perspective; it can lead to an examination of contrary passages hoping to justify the NP. It can lead to almost anywhere BUT a discussion of how old the earth is (which I have gotten tired of elsewhere).