The Pilgrim's Progress is a beautifully written book in the writing style known as allegory. On the surface it seems as though it is but an exciting adventure tale, but to those familiar with the Bible and Protestant theology, one recognizes immediately that there is far more to this story than appears on the surface, and it really serves the Christian as both a cautionary tale, teaching the Christian how to recognize error, and a tale of the assurance and victory the Christian has in Christ Jesus.
Protestant theology is most certainly front and center throughout the story, though to those unfamiliar with how to "read" the text beyond the text, and those who may not have a familiarity with Protestant Theology, it may remain somewhat hidden, I have found Barnes and Nobles texts to be one of the best, containing extensive notes by David Hawkes, which are overall very accurate. It also contains numerous references to Bible passages where the story is drawn from. For instance, in one scene, Christian, with the burden still on his back (i.e. sins), enters the slough of despond, and is pulled out by one named Help to solid ground (cf. Psalm 40:2)
The tenets of Sola Gratia, Sola Fide, Solus Christus, Sola Scriptura, and Soli Deo Gloria are all well-represented and defended within its pages, but especially Sola Fide, and this Protestant Theology, understandably, may be off-putting to Roman Catholics.
That said, as an Evangelical Catholic (i.e. Lutheran), I believe every Roman Catholic ought to read it :)
John Bunyan was heavily influenced by Martin Luther's "A Commentary on the Epistle to the Galatians" and anyone familiar with St. Martin's text, recognizes almost immediately the theology and St. Martin's profound influence on John Bunyan, and hence, the Pilgrim's Progress.
If there is any particular passage one ought to be quite familiar with it is the passage in which a man by the name of Ignorance is introduced - he is, perhaps, one of the most terrifying characters of all, for so many follow his path . . .
May we instead all follow the path of Christian to the Celestial City. Amen.
Soli Deo Gloria