I've come across a couple of definitions that are very useful in framing discussions of the Christian Right.
One is a definition, not of the Christian Right, but of evangelical Christians in the American sense, i.e., not in the European sense of Evangelical=Protestant. It's from a footnote in Andrew Bacevich's The New American Militarism (2005):
In contemporary America, evangelical Christians are distinguished by their belief in biblical inerrancy and in the imperative of a personal conversion experience (being "born again"); by their expectations that the Second Coming of Jesus is near at hand; by their commitment to actively preaching the Gospel; and by their aversion to drugs, alcohol, pornography, promiscuity, abortion, homosexuality, and other "lifestyle" choices viewed as undermining the traditional family. Evangelicalism transcends denominational boundaries. Among the principal American Protestant churches that fall under the evangelical rubric are the Assemblies of God, the Church of God, the Church of the Nazarene, the Southern Baptist Convention, various Pentecostal churches, and evangelical offshoots of the Lutheran, Methodist, and Presbyterian denominations.
As I noted in one of my first Blue Voice posts, fundamentalists are a subset of evangelicals. In Bacevich's definition, which I think is a very good one, Pentecostals are also a type of evangelicals. To a large extent, what we know as the Christian Right is made up of white Protestant fundamentalists and Pentecostals.
And there are very conservative Catholics among the Christian Right. Extreme Catholic conservatives share many of the concerns about moral issues of promiscuity, etc. But they would hold on to their allegiance to the Church, the Pope and the Church hierarachy, which to fundamentalists and Pentecostals are all abominations. Perhaps most importantly in terms of theological beliefs, the "born again" experience as conceived by evangelicals would not be recognized as such by Christian Right Catholics, who would insist on communion with the Church as an essential element of salvation.
Protestant evangelicals are not the same as the Christian Right. One can hold the kind of particular religious beliefs described by Bacevich and still support liberal public policy positions, defend separation of church and state (which not so long ago was a strong emphasis for the Southern Baptists!), oppose military adventurism and preventive war, and have serious reservations about the goals and methods of the Christian Right. Many African-American Christians support some form of evangelical Christianity, but few of them find the Christian Right of James Dobson and Pat Robertson speaking for their notions of public policy.
The other definition is from Sara Diamond in Spiritual Warfare: The Politics of the Christian Right (1989):
The Christian Right is a complex coalition of media ministries, political lobbies and missionary groups active in foreign affairs. Because of the overlapping nature of all of its elements, and because the Christian Right is a movement in constant flux, it is difficult to describe the activities of any one group or individual without simultaneously talking about half a dozen other entities and a whole series of public policy issues. Such is the nature of the beast.
The Religious Right is by no means monolithic, but the competing and conflicting elements within the movement appear to be united in a single overall effort: to take eventual control over the political and social institutions in the United States and - by extension - in the rest of the world. ...
This may sound like a hopelessly unrealistic scheme. It is. But the relevant question is not whether the Religious Right will or will not "take over." The relevant question is twofold: to what degree is the movement already making an impact, and at what cost' In pursuit of its political agenda, now much damage might the Christian Right do—to academic freedom, sexual and racial equality within the United States and to the prospects for genuine progressive reforms in U.S. foreign and military policies? (my emphasis)
Diamond is right to emphasize both the fluidity of the Christian Right and the relevant question about their goals. Her reference to "the beast" is undoubtedly a bit of a joke, because a sinister character called the Beast is one of the leading villains in fundamentalist apocalyptic ideas.
Viewing the Christian Right as a political/religious/theocratic coalition composed of Protestant fundamentalists, Pentacostals and very conservative Catholics is a useful and practical definition. One just has to remember that the Christian Right is a movement, not a particular organization with strict membership rules. Many people who share the main theological ideas of the Christian Right may disagree in very strong terms with their politics. Despite their efforts to mimic "diversity", the Chrisitian Right is overwhelmingly made up of white Christians. It may also include people of less rigorous religious standards who favor the Christian Right approach for political or emotional reasons than religious ones.
And, like any political movement, the Christian Right attracts its share of opportunists, scamsters, hypocrites and assorted hangers-on.