First, let me point out that Phil Jenkins is a secular researcher at Penn State University, and by casting this as Protestant v. Catholic, he’s probably tying to stir up trouble.
But...
(I speak of Brazil because I learned much when the pope was going to visit)
If this were the Lutheran or Anglican/Nigerian church growing so much in Brazil, I could see it as a good situation. Much of Brazil was never Catholic, but simply a mix of unevangelized African and indegenous religions simply labeled Catholic because the nation was officially Catholic. There usually was at least some blending with Catholic / Christian beliefs.
The problem is that most of the new Protestant groups are very dissimilar to the Protestant missionaries who partly evangelized them. Several combine the 7th-Day Adventists’ paranoia against the powers of this world (which in Brazil means the USA), the Pentacostalists’ gnosis and fake prophecying, and the African religions’ fixation on Satan, and a Mormon-like restorationism (that isn’t directly related to LDS) into a horrific concoction that isn’t remotely Christian, but bitterly, even insanely anti-Catholic.
Fortunately, much of this happened in the 1960s and 1970s. Throughout John Paul’s reign, Brazil has strengthened the authenticity and native character of its priesthood (so it isn’t do-gooder liberal religious orders), squashed the Liberation Theology movement, gotten more media savvy, and confronted the radical quasi-Christian movements, so that the number of “Catholics” in Brazil is about the same as it was in 1990, and those who are Catholic are better catechized. That said, there is of course, the same problem with the media promoting sinfulness that we have up here.
I don't know if you're aware of how these things are connected, but they are - specifically, by New York's Hudson River valley and the "burned over districts" of the 19th century.
Throughout the 1800s, numerous revivals swept through the Hudson River Valley in upstate New York. Charles Finney, perhaps the most famous of the "Second Great Awakening" evangelists who repeatedly worked that area, coined the term "burned over district" because the residents had grown increasingly calloused and resistant to his methodical revival methods. He likened them to the charcoal remains left behind by multiple forest fires (the fires being his revivals).
Here's where your connection comes in. Numerous religious movements were spawned in the Hudson River Valley, following those revivals. Adventism, Unitarianism, Mormonism, Restorationism, and scores of other movements Christian and not sprang up or hit the area within the span of a few decades. A common theme among them was that the Catholic Church was to blame for a "great apostasy" in Christianity, and that [fill in the new group's name] was "restoring" the gospel and the "true church" to the world. A lesser theme for many was supernaturalism and prophetism.