This is an argument that deserves more consideration. The thesis is that evangelical Christianity gained adherents in America not because of its theology, but because of its politics. Focusing on the trial of the Rev. William Sloane Coffin, Jr., charged with conspiracy to aid avoidance of the draft, the argument is that church members left denominations which were against the war, and went with denominations that supported the war. In other words, the split between "liberal" and "conservative" Protestants was over politics, not theology.
Which is pretty much what the Rev. Dr. King was pointing to in his letter from Birmingham jail. And it is now the explanation for why so many evangelical church leaders have embraced Trump in a bear hug they can't relinquish. This is sort of interesting, too, because of what I ran into in my brief stint as a parish minister:
A significant number of ministers, for example, championed civil rights efforts and affirmed interfaith cooperation with Catholics and Jews – efforts staunchly opposed by many of their congregants.
In the late '90's I had a church member gravely upset by my use of the title "Prayer of Our Savior" for "the Lord's Prayer." I hadn't thought much of it; it was the title given the prayer in the UCC Book of Worship and commonly used at my UCC seminary. She, however, was convinced that it was a Roman Catholic usage, and that I was secretly an agent of the Roman Catholic church. This was further proven by my use of liturgical worship, which was historically part of the UCC through the German Evangelical (no, not THAT "evangelical") & Reformed traditions, which were in part Lutheran (Lutherans and Anglicans both follow the classic Christian liturgical traditions). The worst insult she could think to hurl at a minister or a church idea she didn't like was to call it "Catholic." That struggle didn't end, in other words, in the '60's.
If you look at this alone, the thesis of the argument seems pretty solid:
Mainline Protestant denominations, however, did not fare as well. They went into decline, losing nearly one in six members between 1970 and 1985.
Most Protestants can't tell you what their denominations position on the Trinity is, or on communion, baptism, what sacraments are (and aren't), and even some "evangelical" churches are starting to talk openly of Lent and Advent as seasons of the church that help organize worship across the calendar and keep every Sunday from being the same service as last Sunday. But they can tell you what their denomination's stance on immigration or the death penalty or abortion or even gay rights is, and I have no doubt most people leave their churches over those issues than over the theological, ecclesiological, soteriological, or Christological stance the minister brings to the pulpit