What is the theological significance of the label "Christian", according to evangelicals?

independent of other doctrinal differences

That's definitionally impossible. Every group must have a baseline "ring" around the group defining who's in and who's out.

An explicit example would be someone who says, "I'm Jewish just because I claim to be Jewish." It just doesn't work that way.

Of course, the word "Christian" only means "follower of Christ", so is woefully non-specific. That's why each denomination (and -- in reality -- each person in a country like the US) must decide where that ring is.

I debated if this should be an Answer, as I go into specifics more than any general answer. But I think it gives insight to your question by pointing out groups that are not considered to be Christians by many or most Evangelicals, and why.

You specifically mention the Church of Jesus Christ of Latter Day Saints or Mormons as a group that Evangelicals do not consider to be Christian. The doctrinal difference there is basically everything in the Book of Mormon and other Mormon-only books. Evangelicals tend to be Sola Scriptura, or Scripture Only, and do not think you can add any books beyond the 37 in the Old Testament and 27 in the New.

There is also the issue of the Founder, Joseph Smith, whose claims of divine inspiration they reject. They tend to believe he was a swindler. They think his ideas about Native Americans being Jewish people were just made up. His methods of receiving the divine intervention were not the types of ways that revelation was shown to happen in the Bible, but more how psychics and spiritualists at the time would do, e.g. putting his head in a hat with stones. He also supposedly translated some texts with divine help, but the translations do not match what scholars say today.

As such, they see Joseph Smith as a false prophet, and thus his entire movement as false.

Other groups I can think of that are generally not held to be Christian would be the Jehovah's Witnesses. In this case, the doctrinal issue is quite clear: they reject that Jesus is God.

Some also would exclude those who reject the Trinity, such as Oneness Pentecostals. And some do indeed reject Catholics because they have their Traditions being added to the Bible, and the veneration of Mary and the prayer to saints. Also, Catholics reject Sola Fide, or salvation by faith alone.

Finally, I would say Evangelicals and many other self-identified Christians reject those who identify as Christians because they follow the teachings of Jesus but argue he was just a man. These groups have various names. My high school friend refers to herself as a "Progressive Christian."

I take "evangelicals" to mean Protestants. Within Protestantism, the term "Christian" is both theologically and socially significant, and has come to refer to the collection of individuals and churches that form the Body of Christ.

But just as Protestant doctrines are not completely uniform, each Protestant denomination and even individual churches within the same denomination could decide differently whether this or that other sect (the Mormons, Christian Science, etc.) has sufficiently correct doctrines to be considered part of the Body of Christ, or the catholic (little 'C') church.

In general, Protestants will tend to look skeptically on a church that deviates from mainstream in the following ways:

• Additional text considered to be Scripture that is not part of Protestant canon (belief in the authenticity of the deutero-canonical books can be considered acceptable)
• Refusal to accept as Scripture any text that is part of Protestant canon
• Heavy, undue emphasis on non-Scriptural texts, even if that teaching is not considered to be Scripture
• Appearance of having a cult of personality, in which the instruction or teaching of past or present leadership is given similar weight to Scripture itself
• Zealous preference for a particular translation of Scripture done "in house" and therefore substantially different in content from mainstream translations
• Any doctrines that plainly contradict the Nicene Creed and/or the Apostles' Creed - especially the humanity of Christ, the divinity of Christ, the death and resurrection of Christ, and the imminent return of Christ
• Any doctrine that teaches any means by which mankind can be reconciled into fellowship with God, other than the sacrifice of Jesus Christ
• Any novel practices, rituals, etc. not supported by Scripture or tradition, that are taught as required; or forbidding things that Scripture does not forbid
• Any attempt to insert people or idols as intermediaries between the individual and God; Jesus is the only mediator between man and God
• Any sect that concludes, by way of their doctrines, that your denomination is not part of the Body of Christ due to your authentic doctrines or practices is therefore suspicious

I'm reluctant to start listing disputed doctrines, but it should be plain to see why according to the above criteria certain organizations would draw skepticism from many Protestants: LDS, Christian Science, HaShem's Witnesses, Universalism, etc.

However, there are degrees, and even within mainstream denominations, individual congregations can draw skepticism, but usually not accusations of being "non-Christian". Specifically, 'megachurches' with celebrity pastors sometimes start to look like cults, especially when the pastor's books seem to get as much or more attention than the Bible itself. And some groups have mainstream doctrines, but non-mainstream practices (Seventh Day Adventists, Amish, Mennonites) or highly insular cultures (Church of Christ Boston movement) that draw skepticism from others. Also, even though today's Protestant denominations all draw lineage from the Protestant Reformation, today many (but not all) Protestants recognize Roman Catholic believers as being Christians, just with many misguided doctrines.

(You will recognize in the above list a kind of definition of what it means to be Protestant. Scripture alone is the authority on doctrine, not the church or its human leaders. Every believer is a priest, and Jesus Christ is our priest; we need no other priest. God's grace, Jesus' sacrifice, and our faith are all that is required for men's salvation; not sacramental rituals. And so on.)

Directly answering the question now, the term "Christian" is both theologically and socially significant. There is a mainstream Protestant theology, outlined as well as anywhere in the Apostles' Creed; and there is a mainstream Protestant culture which is essentially a modification of Roman Catholic practices to bring them in line with Protestant doctrine. A general Protestant definition of "Christian" must be a 'fuzzy' one, and there will be differences of opinion between denominations and between individuals regarding certain groups.

Is there any theological significance attached to the label that causes this reluctance to grant the label Christian (according to evangelicals)? Or are there non-theological reasons?

I think the simplest answer could be expressed as "brand recognition". I'm also a technology fan, so to use an analogy, let's say we're talking about "IBM-compatible computers". When you see something labeled "IBM compatible", you might reasonably expect certain features, such as a given CPU architecture and compatibility with "standard" peripherals (disk drives and expansion cards).

Now consider a Sun workstation (circa 1990, i.e. before Solaris moved to x86). It uses a different architecture and doesn't accept the same peripherals. If I were to tell you this machine is "IBM compatible", you might have good cause to be annoyed, because it doesn't fulfill the criteria you expect from that "branding". My doing so, in a sense, is harmful to the "brand reputation".

Among religions, those commonly labeled "Christian" have certain features; particularly, beliefs about the nature (and existence) of God and eternity, belief in an entity "Jesus Christ" (who may or may not also be God), beliefs about the mechanisms of Salvation, and so forth.

Mormonism, like the Sun workstation, has "similar" features (both have disk drives, both have a divine entity), but the nature of these features is significantly different. I won't go into details of how LDS differs from Trinitarians and Unitarians, but suffice to say there are significant differences. (Beyond consubstantiation, which also separates Trinitarians and Unitarians, and note that I am considering both as "possibly Christian", despite a fair degree of animosity between even those two groups.)

Thus, to a creedal Christian, allowing an LDS to call themselves "Christian" is not unlike allowing a Muslim or a Buddhist to call themselves "Christian", and possibly worse because the differences are less obvious to an uninformed outsider. In short, it undermines the common theological understanding that is associated with the Christian "brand".

That is a good question. In my experience, the evangelical Christians I know would define a Christian as someone who believes the Gospel as taught in Scripture. As we see in Galatians, the Apostle Paul himself warns against those who would distort the Gospel of Jesus Christ.

The Gospel would generally include at least the following:

1. There is a God who created heaven and earth and who will judge the living and the dead, who is Himself uncreated and eternal

2. This God is a Trinity, and God the Father sent His Son to be the God-man, both fully God and fully man, to redeem humanity.

3. We are saved by grace through faith and not by any good deeds that we ourselves have done.

4. Jesus died on the cross and was resurrected bodily from the grave, and will one day return to judge the living and the dead

Galatians 1:6-9, 11-12

I am astonished that you are so quickly deserting the one who called you to live in the grace of Christ and are turning to a different gospel— 7 which is really no gospel at all. Evidently some people are throwing you into confusion and are trying to pervert the gospel of Christ. 8 But even if we or an angel from heaven should preach a gospel other than the one we preached to you, let them be under God’s curse! 9 As we have already said, so now I say again: If anybody is preaching to you a gospel other than what you accepted, let them be under God’s curse! ...I want you to know, brothers and sisters, that the gospel I preached is not of human origin. 12 I did not receive it from any man, nor was I taught it; rather, I received it by revelation from Jesus Christ.

For a fuller explanation of what it means to be a Christian as defined by evangelicals, check out the Levels of Doctrine Article from TGC. I think this is a pretty typical definition of being "in the faith" - we need to accept certain absolutes in order to be called Christians. Obviously there are groups who are either more exclusive than TGC or more inclusive, but I think this is pretty typical.

1. absolutes define the core beliefs of the Christian faith;
2. convictions, while not core beliefs, may have significant impact on the health and effectiveness of the church;
3. opinions are less-clear issues that generally are not worth dividing over; and
4. questions are currently unsettled issues.