Sometimes evangelicals are called new-evangelicals. Why? At one time, everyone who believed the gospel (the only Scriptural one) were evangelicals. Then liberalism came, a group split and they were called fundamentalists, hence, fundamentalism. Then fundamentalism split over separation issues. The less separated called themselves evangelicals. The fundamentalists called them new-evangelicals. (Incidentally, because of history, everybody gets to claim Spurgeon---we're Spurgeon, they're Spurgeon; no, we're Spurgeon.)
Since then lots of smaller splits have occurred within fundamentalism, partly because of associations and fellowships---GARBC, BBF, Southwide Baptist Fellowship, Sword of the Lord meetings, FBF, etc. Fairly large cleavages have occurred over a general salvation issue which includes soteriology, sanctification, and methodology. One side is more Calvinistic versus the other more Arminian, or in other terms, the Hyles group (revivalist) versus the Bob Jones group with various nuances in between. One side seems to put more into strong academics and the other side seems to emphasize learning new and newer methods. Even though both sides call themselves fundamentalists, they often ignore each other, hoping no one will associate them with the other. Various segments would not want to be identified with the other even based on things that might look minor, like styles or methods of preaching. The version issue in all its forms has strained relations---one side says the other causes division and the other side says their opposites attack God's Word. Another aspect is cultural, dealing with issues of personal separation---pants on women, "evangelistic" music versus worship music, entertainment, the roles of men and women, and even alcoholic beverages. Fundamentalists are feuding.
Many fundamentalists have apparently wearied over carrying a common name. For this reason among others, a lot of professing fundamentalists are looking for more and more common ground with evangelicals (new-evangelicals). Sometimes they feel like they are more tuned into the evangelicals than they are most fundamentalists. In various forums of communication, I have noticed professing fundamentalists admiring evangelicals. Salivate might not be too strong a word. They are far less harsh about certain Southern Baptists or conservative evangelicals than they are over who they see as counterparts in their own movement. Some have taken the leap and others are considering joining them.
I'm going to tell you exactly where the rub is for the fundamentalists, what is bothering them. It is a root doctrinal issue. They teeter uncomfortably on the edge of fundamentalism because of one important cog in their system.
Let's say that you believe that the true church, the church, is all believers, everyone who has received Jesus Christ into his life. I don't believe that. I believe a church is an assembly of immersed believers and only an assembly of immersed believers. I take my position from the 118 times the term ekklesia is found in the NT. But you believe that at the point of justification, you were baptized spiritually into the invisible body of Christ. If the church is the body of Christ, then the members must be working together. Christ is the Head and the body parts, like a physical body, fit and interact, or in other words, have unity.
The [new-]evangelicals are more consistent with their ecclesiology. It's as simple as that. Many fundamentalists have exactly the same ecclesiology as the evangelicals, but they don't unify. They separate. How can we separate from people we're supposed to be unifying with? John MacArthur gets along with Al Mohler who gets along with Billy Graham. They are all together for the gospel. Yes, the gospel. They are all "saved," so they get along. These fundamentalists want that unity because it is consistent with their ecclesiology, their belief about the body of Christ. They know they aren't consistent in their practice. They essentially make the Bible contradict itself with their stand on separation and on unity. Conversations and arguments and debate regularly spring up on the conflict between separation and unity.
If I believed the body of Christ was all believers, I would fellowship with the evangelicals. My only grounds for separation would have to be the gospel. You are either saved or your not. If you're saved, I'm fellowshiping with you. The fundamentalists don't do that. They break up the body of Christ (their view of it) over issues. Where is the unity? Hard to say. Maybe with other Bob Jones graduates and those who approve of Bob Jones.
Some try to be more consistent with unity and put up with Pensacola, who isn't in the Bob Jones orbit. They get criticized for it mightily. Letis, video tape, and heresy comes up. Some try to travel in everybody's fundamental circle. I don't think anyone has done that successfully. Now among fundamentalists, the worst group to be associated with are those who are King James only. It is open season to shoot at all KJVO'ers. If they're saved, that's not consistent, is it?
Evangelicalism feels so good because it snuggles right in with spirit baptism and the universal church. Most evangelicals look at fundamentalists as sort of goofy because of this inconsistency. Of course, the conservative evangelicals are haunted by their lack of separation, but unity beats separation almost every time. If they don't participate in Promise Keepers, it's a preference. They're still together with them. They have to be. They're just showing discernment. They don't want to get hurt by being with these fellow believers, yet with no formal separation. On the other hand, I don't know how fundamentalists could possibly argue against evangelical unity with their ecclesiology. The evangelicals definitely have this one on them.