This is hard to answer because of the slipperiness of the term “liberal.” First, it was never clear whether it means politically liberal or theologically liberal. While at one time conservative theology meant political conservative, there are now moderate evangelicals that understand Jesus’ priorities to imply something that in the US is considered politically liberal. I think of "progressive" as being associated more with the political implications. I connect "liberal" with an approach in theology and exegesis that was associated with the word "liberal" back into the 19th Cent.
Second, in my opinion there are two different kinds of theological liberal. One is someone who has simply become skeptical about traditional theology. They may not have anything specific to replace it, but they have this feeling that Jesus wouldn’t agree with things like 90% of the people going to everlasting torment, and that things like the Trinity may not represent Jesus’ view. Although this isn’t my approach, there are people in my church like this. I think such people are common even in more conservative churches. The survey data I see on attributes of younger Christians about gays suggests that the number of people like this is growing.
The second type of theologically liberal are people who follow the official theologies of the mainline churches. These go back to 18th Cent developments in scholarship, which began to have significant impact in the US in the late 19th Cent, leading up to the early 20th Cent church conflicts. These folks tend to see Scripture as a description of human encounters with God, but not in itself God’s word. (One phrase is "Scripture contains the Word of God," though that's not a phrase I'd use.) They accept modern scholarship on Scripture. They also accept modern theology, which sees traditional theology as attempts of Christians in various cultures to understand and apply Jesus teachings and the impact of his death and resurrection. But as we’ve come to understand more about the Jewish background of the New Testament, it’s clear that this theology at times misunderstands the intent of the Biblical authors.
I represent the latter type of liberalism, so I’ll talk about it. In my opinion the range of views represented go roughly from N T Wright to Marcus Borg. Wright is considered a conservative in the UK and Europe, but in the US context he’s a liberal. In particular, he rejects Chalcedon, the key definition of the Incarnation, because he doesn’t think it uses Biblical categories.
In my experience, all liberal theologians accept key Christian doctrines, such as the Trinity and Incarnation. However they don’t understand them in the way that they ended up being formulated officially. The Incarnation as officially described takes an approach that is commonly called “ontological.” That is, it’s based on the kind of metaphysical entity that Christ is. In particular, he is a person with two natures. Most modern theologians don’t use that type of description, and believe that the NT authors didn’t intend it. They see the unity between Jesus and God to be “functional.” That is, Jesus is spoken of in the NT as God’s way to be present with us. He functions as or for God. Another approach, which you’ll see in Wright, says that Jesus is part of the “identity” of God. If you’re interested in more, see Wright’s paper
Jesus and the Identity of God. Wright has rather pointedly refused to answer the question of whether Jesus is God, because he doesn't think that's the right way to put it, but denying it is likely to imply things he doesn't want to imply.
Key questions:
* What’s the role of Scripture? As I noted, I think God actually did send Jesus, and that he did actually guide Israel, at a minimum through the voice of the Prophets. The Bible contains the only primary source data for understanding that. Yes, it comes from a culture that’s more credulous about miracles, and many of the NT documents probably make false claims about their authors, but I still think it’s hard to explain the existence of Christianity without thinking that something like that actually happened. So despite its limitations, our theology still has to be based on Scripture. It’s just that we need to assess each book in the Bible critically, to understand how it can and can’t be used.
* Do we actually believe in God, or is it a metaphor? That’s a difficult question. As far as I can tell, mainline leaders and the theologians they work with actually believe in God. There are people further out than Borg, who I think do use God as kind of a metaphor. But Borg himself says clearly that he thinks there’s something beyond this world, with an actual God that does things. I’m part of a pretty liberal church in the Northeast US. I’m reasonably sure that our members and clergy believe there’s an actual God, and do normal things like pray. Of course there is one minister in my denomination who is an atheist. I don’t deny that there are more radical people. But I don’t think very many liberal Christians go that route.
A trickier person to deal with is Spong. He says he doesn't believe in a "theistic God." He seems to be rejecting the idea that God is kind of like a human being outside the universe, who reaches in an intervenes. It's a bit unclear what his alternative is. Someone reading his work could reasonably accuse him of making God essentially a metaphor. I'm not going to make a judgement, because I can't tell what he's actually advocating. I think this view is unusual within mainline Christianity. (By mainline I mean the traditional liberal denominations: Presbyterian, Methodist, Episcopal, Lutheran, etc.) But maybe if I understood what he meant I'd be more accepting. I note that with this view it becomes hard to say that humans are made in God's image, even though this is something he wants to say.