What would make a fundamentalist reject or reclassify some of his fundamental brethren as "neo" fundamentalist, and why would they want to discuss separating from them?   
Let me begin by saying that the doctrine of separation could fill
books, and this is an introduction according to my neophyte
understanding of the matter.  For some more depth, visit my friend Neofundametalist.

There are at least four ways to describe or view the doctrine of separation, and this may clear up why, how, and when we should separate from certain people.  These scriptures and doctrines definitely apply to the scores of Episcopalians leaving the mainline church because of it’s pro-homosexual stance.

1. Gradeschool Level:  The simple biblical references

The bible specifies instances when we should separate ourselves from fellowshipping with certain types of people.

I wrote to you in my letter not to associate with sexually immoral
people – not at all meaning the sexually immoral of this world, or the
greedy and swindlers, or idolaters, since then you would need to go out
of the world.But now I am writing to you not to associate with anyone
who bears the name of brother if he is guilty of sexual immorality or
greed, or is an idolater, reviler, drunkard, or swindler, not even to
eat with such a one. (1 Corinthians 5:9-11)

Note first that this does not apply to non-Christians.  Biblical
separation is about how we approach sin in the church.  So, if a
professing Christian is unrepentant in any of these sins, Paul said
have nothing to do with him, don’t even eat with him. But to get to the
point where we have ascertained he is unrepentant, we should go through
the pattern of biblical Church discipline
first:

If your brother sins against you, go and tell him his fault,
between you and him alone. If he listens to you, you have gained your
brother. But if he does not listen, take one or two others along with
you, that every charge may be established by the evidence of two or
three witnesses. If he refuses to listen to them, tell it to the
church. And if he refuses to listen even to the church, let him be to
you as a Gentile and a tax collector.(Matthew 18:15-17)   

Rather than being something cruel, however, Paul explains that this
type of "shunning" or "disfellowshipping" is for the restoration of the
person, not out of spite:

If anyone does not obey what we say in this letter, take note of
that person, and have nothing to do with him, that he may be ashamed.
Do not regard him as an enemy, but warn him as a brother.(2
Thessalonians 3:14-15)

Brothers, if anyone is caught in any transgression, you who are
spiritual should restore him in a spirit of gentleness. (Galatians 6:1)

In fact, in the specific instance where Paul required the church at
Corinth to do this to a man who was sleeping with his step-mother, Paul
later adjures them this way:

For such a one, this punishment by the majority is enough, 7so you
should rather turn to forgive and comfort him, or he may be overwhelmed
by excessive sorrow. 8So I beg you to reaffirm your love for him. (2
Corinthians 2:6-8)   

So, these are the main scriptures that define the doctrine of biblical
separation
– separation from

  • Those who are teaching that which is clearly false doctrine
  • Those who are walking in rebellion (refuse to repent)

2. Highschool Level:  In the essentials, unity

However, if we were merely to take a list approach to what issues we
should separate on, that won’t work.  I mean, what is "false
doctrine"?  So here’s an intermediate approach to defining what we
should separate over.  The well-worn Augustinian statement below is one
of my favorites

    In the essentials, UNITY
    In the non-essentials, LIBERTY
    In all things, CHARITY

This formula basically asks us to identify the essential doctrines of
Christianity, and to separate ourselves from those who call themselves
Christians but do not believe in these essentials.  This is as much
practical as it is doctrinal.  The main problem here is with those who
make their list of essentials too broad, which in effect eliminates
everyone except those who agree on every point.

In fact, if we demand that some of the non-essential doctrines be
essential, then we are really "majoring on minors", to our own hurt.
So what are the essential doctrines?   I have three things to say about
this:


a. The creeds are not lists of essential doctrines

Though creeds are nice summaries of what Christians believe, they can
omit key doctrines or include non-essential ones.  For example, the Nicene
Creed
omits the deity of Christ.  The Westminster Confession
of Faith
(my favorite) is very long, but includes many doctrines that are not
essential.  But the general principle is, try to make
this list as small as possible in order to broaden fellowship among
believers.

I mean, I think I would limit it to ‘if you believe you are a sinner
and Christ died for you, and you have asked him into your heart and
life as savior and lord, and have witnessed an internal change towards
holiness and rigtheousness" then I’d say let’s hang out.  Or, if you want something a little longer, I once mentioned this
seven point list
as a good one

   1. The Deity and Humanity of Christ
   2. The Trinity
   3. Original Sin
   4. The Substitutionary Atonement
   5. The Resurrection of Jesus
   6. Justification by Faith Alone
   7. The Second Advent of Christ


b. One of the errors of traditional fundamentalism is to include too
many non-essential doctrines in their "essentials" list, and to include
unbelievers in our separation.

Not only did fundamentalists make their list too long, and thereby
overly stress absolute unity, they often included modern behaviors such
as dancing, smoking, drinking, card playing, and movie attendance.
Also, their isolationist tendencies were buttressed by their
eschatology, and so they withdrew from popular culture and politics,
pretty much only talking with themselves.


c. We must follow the guiding principles of Romans 14 to navigate moral gray areas.

Rather than lists of don’ts, we need to follow Pauls
worthy advice
given in Romans 14.  ‘Nuff said.

3. College Level:  First and Second order Doctrines

The idea of essential and non-essential doctrines is a much more
esoteric discussion than most would like to admit.  For example, see
the posts over at NeoFundamenatlist on this subject entitled such
things as First
Steps to a Second Order Taxonomy
.  But the basic idea behind
these ideas is that we can’t actually make a definitive list of
doctrines, but we can make a list of guiding principles that can guide
us to a good approximation.  One example of such principles are:

  • Doxological purpose – the more essential a doctrine or practice is
    to this doxological purpose, the more essential it is for fellowship.
  • Christological purpose – the more essential a doctrine or practice
    is to displaying the humility and love of Christ, the more essential it
    is for fellowship.
  • Revelational purpose – the more essential a doctrine is for a
    proper response to Scripture, the more essential it is for fellowship.

So, if we are guided by the hard to understand principles above, and
don’t have a definitive list, what can we say?  Only that separation is
a not a binary either/or, but rather, a gradient that
goes from absolute separation to increasing fellowship.  The more we
agree, the more unity and fellowship we have. 

What does this mean for separation in practical terms?  Probably that
we have very limited actual fellowship with those whose doctrines are
very different than ours.  However, some things such as unrepentant sin
are clear, and we should have little difficulty identifying these
(unless we are in the gay apologetic camp).


4. Post Graduate Level:  First and Second order Separation

First order separation is separating from other Christians when they
teach or practice bad essential doctrines or sin.  But what if they are
good Christians in our view, but *they* fellowship with the *bad*
Christians?   Should we separate from them because they refuse to obey
the biblical doctrine of separation from unrepentant believers?  This
latter separation is called Secondary Separation.  Is it important?  I
would say that’s up to each believer.

CONCLUSION

Most evangelicals don’t even know about the doctrine of separation,
much less preach or practice it.  In fact, most modern evangelicals are
totally unaware of the history of their own movement, which broke away
from the funamentalist movement in the 1940’s.  This breakaway led to a
whole discussion among fundamentalists about whether or not they should
fellowship with these breakaway Christians, or be truly "separate" from
them.  Hence the doctrine
of separation
was born.

But what is important to me is not a definitive list of essentials (but
a list is still useful), but how much unity can we build before we
start accepting outright heresy?  I mean, when the Episcopal church
ordains gays, I’d say they are condoning sexual sin, and we should
leave their churches.  This schism only has one way to go for biblical
Christians, which is separation from such obvious apostates.  If they
want to justify sin in the name of Christ, that’s their business, but
we should have no part with them, even if some of them are genuine, if
unenlightened, Christians.  The goal?  That they might also separate
themselves from this darkness and be restored to the light.

I also think that, since these are not simple matters, we should
maintain an attitude of humility, even while refusing to fellowship
with certain groups, because we may be wrong in some or all of our
particulars.  NeoFundamentalist admits such when he says

  • Mercy of God – we should be full of mercy and compassion
  • Justice of God – we should be fair and just in our dealings, but without vengeance
  • Righteousness of God – we should do what is right, regardless of who we offend (on either side of the spectrum)
  • Goodness of God – we should strive to edify and build up those who hear us
  • Faithfulness of God – we should practice what we preach
  • Longsuffering of God – we should put up with and bear with
    otherís ignorance and errors, rather than simply throwing away those
    who disagree with us
  • Truthfulness of God – we should not shy away from proclaiming the truth, as best as we can discern it
  • Love of God – we should speak only for the benefit of others to the glory of God

This post may not have made everything clear, but again, it’s my neophyte understanding of this interesting phenomenon.