Noll and Nystrom, in their Is the Reformation Over?, chp 3, see the shifts that occurred in the 1950s to concern four, yea five, things: changes within the Catholic Church, in world Christianity, in American politics and society, in the exercise of personal agency, and within evangelicalism. A word about each.
Vatican II: David Wells, in the aftermath of V2, saw major changes in revelation, relation of the natural and supernatural, salvation, doctrines of the Church, papal authority … making obsolete many contemporary Protestant analyses of Rome. V2 created the need for Protestants to reevaluate their entire apologetical and polemcial frameworks with respect to the RCC.

World Christianity: the global growth of the Church led to tolerance in non-threatening areas. Ecumenical breakthroughs occurred where the danger of assimilation was not a threat. Worship styles helped along with evangelical youth movements. Discovery of GK Chesterton, JRR Tolkien, etc.. Each played a part.
American Politics and Society: JF Kennedy. “Ecumenism of the trenches” (T. George) where evangelicals and Catholics have worked side by side. JP2 and the demise of dictatorial rule in Poland (previously, American Prots thought Catholics supported dictators). Cultural wars over sex, self-defense, and economy have drawn RCs to evangelical Protestants.
Personal Agency: decisive influence from charismatic individuals and the Vatican’s reaching out to all sorts.
Changes within Evangelicalism: Tom Howard’s conversion to RC from being an evangelical at Gordon College is but one example of many who have converted (Noll-Nystrom mention my article here favorably; you can find it on the Sidebar: “From Wheaton to Rome”).
These five changes have led to a major shift in relationships between RCs and Evangelical Protestants — without denying differences, many of the old edges are gone and many old debates have been settled.
Tomorrow: Ecumenical Dialogues.