This is a really interesting question, and even though I grew up evangelical Protestant, and did not convert to Catholicism until I was 47 years old (8 years ago), I honestly don’t know the answer.
I would suggest that the OP get hold of the classic work by Francis Schaeffer,
How Shall We Then Live?" books.google.com/books/about/How_Should_We_Then_Live.html?id=9bR8xRzvNpQC
I remember when I was a teenager, that our pastors and teachers warned us about the “liberal theology” being taught in the mainline Protestant churches. That would have been in the late 1960s and early 1970s. I believe it was in the 1970s that the first women pastors showed up in the United Church of Christ, and this denomination was also the first to ordain openly homosexual men to the pastorate and proudly announce it to the public media.
We also observed that several of the mainline denominations stopped teaching the literal resurrection of Jesus Christ, and began teaching a symbolic resurrection of the “principles” taught by a loving Jesus (who was probably gay, according to these churches).
The Virgin Birth also was jettisoned, along with all the other Biblical miracles.
OTOH, these older mainline churches began extensive social gospel outreach. Many of the churches were located in downtown (urban) areas, and so were in a prime position to start up food pantries, soup kitchens, thrift shops, free clinics, after-school care, low-cost pre-schools and day cares, etc. Many good people, especially wealthy people, were attracted to these churches because of their work among the poor, although for the most part, these theologically-liberal churches lost hundreds of members beginning in the 1970s.
Meanwhile the evangelical churches, which were theologically-conservative, were located in the “burbs,” so we weren’t in a position to do much hands-on work to help the poor. Sadly, this became a point of contention between “us” and “them,” and many of us came to be suspicious of social gospel because all too often, the churches who practiced it did not teach a true Christian Gospel of Jesus Christ crucified, risen, and coming again.
Tony Campolo came along at this time and started chastising the evangelical churches for avoiding the social gospel out of fear of theological liberalism. He’s still around, and he’s still a force to be reckoned with. I happen to like him, but I know that a lot of evangelical Protestants are suspicious of him.
However, beginning in the 1970s, the evangelical Protestant churches began to grow in leaps and bounds. I remember attending conferences in which the phrase “exponential growth” was described. This means that a church would double, then double again, and again, etc. We saw this happen at the church we attended in college, which grew from about 100 members to well over 500 members in three years.
Many of the people who were joining evangelical Protestant churches were refugees from the mainline churches who were fleeing the liberal theology. Often these refugees were breaking ties with churches that their family had attended for several generations, and it was tough for them.
I see this same thing happening now in Catholic parishes–former Protestants are fleeing to the Catholic Church because we want to escape from the simplistic sola Scriptura praise and worship fellowships that many of our evangelical Protestant churches have become. Or people who stuck it out in the mainline Protestant churches back in the 1970s and 1980s are now finally realizing that their churches are lost in liberal and even heretical theology, and so these families are breaking ties and becoming Catholic, where the teachings are still conservative (theologically) and orthodox.
I think we need to be careful to differentiate ECONOMIC conservatism/liberalism from SOCIAL conservatism/liberalism from THEOLOGICAL conservatism/liberalism. So far in this thread, I think that sometimes these three are being blurred.
I personally do not think that a church can be theologically-liberal and still be called “Christian.” When a church teaches such things as “Mary was not a virgin when she gave birth to Jesus” and “Jesus did not really die on the cross, therefore he did not rise from the dead,” and “the Bible is just a book written by men,” and “there is no sin,” or even, “God is not a person, God is within us”–these teachings are not consistent with the Christian teachings passed down from the apostles, and I don’t see how a group that teaches these things can be called Christian. This group may do many good things in the community, and be a beacon of hope to the poor, the sick, the disenfranchised, etc.–but it’s not Christian!
Also, there are churches that are theologically conservative, but economically-liberal–they are suspicious of capitalism and open to the re-distribution of wealth. Many of these fellowships believe that communal living is THE Biblical way of life for Christians, and argue that capitalism is opposed to the teachings of Christianity. Here on CAF, and also in real-life in my parish, I meet up with Catholics who seem to lean this way.
I don’t know of any churches that are theologically-liberal but socially conservative–usually churches that teach that “Jesus was just a really good teacher” are also supportive of abortion, homosexual marriage, etc. because they don’t have any guideline for morals, and have rejected traditional moral teachings. But I suppose it’s possible. Anything’s possible.
So the conclusion that I would make from my own musings above would be that the churches that became THEOLOGICALLY-liberal back in the 1970s have become SOCIALY and ECONOMICALLY-liberal in the 2000s. But I would not want to commit myself to that answer until I read what others have to say, and also check out Schaeffer’s book.