There are two answers to this question. One is the general type of "Cultural Christianity" to which other answers alude. A person can be non-religious, but still operate in a largely Christian context, clebrating some Christian-flavoured festivals (notably Christmas), and thinking of "God" in a Christian context, even without necessarily believing in that God. Richard Dawkins is such a cultural Christian, and is happy to talk about it.
But it's also possible to be deeply religious (a word which is notoriously hard to define) within a Christian context without taking the beliefs literally. Mysticism is not confined to "Eastern religions" and Neo-Paganism. There are also mystic traditions within Judaism, Islam, and Christianity.
Since you mention Judaism in your question, let's talk about that.
The "Cultural Jews" you mention may not be simply thinking of themselves as Jews. They may also follow many Jewish traditions, keeping strict kosher, following Sabbath law, and suchlike, and find great meaning in those traditions, without necessarily believing in God. Mystic traditions often find the question "Is this really true?" to be quite uninteresting. What matters to them is whether it's useful, and whether it's meaningful. Many people can find great meaning and beauty, and a sense of connection and deep mindfulness, with the tradition of Judaism, without really caring whether God exists. This is clearly a step beyond simple "Cultural Judaim". It's a religious practice. A deeply felt, important, sincere religious practice. And yet it meets your criterion of "not interpreting the religion as a fact".
This experience is perhaps most well known within Judaism, which is why I've used that as my example, but it certainly exists also within Christianity (and Islam). So there is a larger answer than "Cultural Christians". There are many varieties of mystic and semi-mystic experience, which may take Christian beliefs more or less literally. Some don't take them literally at all. And many don't see that question as important.
(Of course, some people have a mystical approach to faith while also taking it literally. Mystic does not necessarilly imply non-literal.)
Syncretic Neo-Pagan faiths can also operate in a somewhat Christian contexts. Wiccans may possibly draw on Christian figures. Vodoun is probably the most Christain-influenced form of Neo-Paganism (certianly the most Christianised one I know of). These faiths probably wouldn't be refered to as "Culturaly Christian", or, indeed, as Christian at all, but everything exists on a spectrum, and religions and cultures bleed into one another. (All categories have fuzzy edges, as I've said before.)
So the answer to your question is manyfold: Christians who don't take the belief literally include,
- the "Cultural Christians" mentioned in other answers,
- Mystic Christians,
- Semi-mystic Christians,
- people who find meaning in Christian practice, but who wouldn't necessarily believe it or call themselves mystics,
- Neo-Pagans who are stronly enough influenced by Christianity that they might possibly be counted as Christians themselves,
- people who use Christian teaching as an ethical framework, without necessarily believing in anything supernatural,
- and others.
All shall be well, and all shall be well, and all manner of thing shall be well.