So, as a broad approximation, liberal Christianity is Christianity that is acutely alive to the challenges to belief coming from modern philosophy. Kant’s denial of knowledge of the noumenal realm apparently made traditional accounts of revelation impossible, and the more-or-less simultaneous rise of Biblical criticism made traditional accounts of revelation profoundly precarious even if possible.So we see a philosophical challenge that we might call modern skepticism. How can we know anything beyond the senses with certainty? Anything about God, anything about right or wrong, anything about how things are meant to be? We also have a biblical challenge. Lots of historical and linguistic research was shedding new light on the bible and questioning it from new angles. So having the bible as the foundation of your world and life view was not working that well.
One reaction to this was fundamentalism. It is actually only a few centuries old. It puts the focus on faith. Just reject all the research you don't like. Faith becomes a trump card that can defeat any rational objection. A rejection of evolution in favor of a literal interpretation of Genesis was a classic example. Dismissing scientific arguments based a a verse of scripture became a virtue.
Liberal Christianity didn't go there. Where it did go is unclear. Holmes said it based itself on "shared religious experience" and thought Schleiermacher was the key thinker. That strikes me as kind of lame. Every community has shared experience, some of it good and some of it bad. But that hardly counts as a basis for a religion. For a club maybe but not a religion.
What makes liberal Christianity hard to define is the lack of a foundation. It mostly believes in scripture. It mostly believes in reason. It tries to focus on action rather than theology. This is because its theology is either borrowed from the culture with religious language injected or it is a critique of fundamentalism. It really does not have a basis for its own theology.
So Douthat was being kind in just identifying liberal Christians as those who do a lot of social action. That is how they like to be thought of because that is when they are at their best. But fundamentalists and Catholics do social action as well. Liberal Christianity really can only be defined negatively. It is the faith without content. What CS Lewis called "men without chests."
Talking about fundamentalism and liberalism, I should not neglect to mention that Catholicism has the best of both worlds. That is it has infallible doctrine but no doctrine contradicted by science. We have help. The Holy Spirit keeps us from defining falsehood as dogma. Biblical criticism is easier for us to deal with because the bible is not the foundation of the Church. Again we had help. Jesus cleverly built the church on the rock of Peter and not on the scriptures as its basic foundation. So the successor of Peter can define how scripture is to be read. Pope Benedict XVI has said that his Jesus of Nazareth books are, in part, an example to all Christians on how to do proper exegesis, how to use historical criticism, how to avoid hyper-skepticism, how to incorporate the unity of the whole of scripture and tradition, etc.