Division in the Church

Romans 16:17-18
I urge you, brothers, to watch out for those who cause divisions and put obstacles in your way that are contrary to the teaching you have learned. Keep away from them. 18 For such people are not serving our Lord Christ, but their own appetites. By smooth talk and flattery they deceive the minds of naive people.

DIVISIONS - Dissensions; parties; factions; 1 Cor 1:10-13; 3:3; Gal 5:20. The very "attempt" to form such parties was evil, no matter what the pretence. They who attempt to form parties in the churches are commonly actuated by some evil or ambitious design.
(from Barnes' Notes)

Contrary to the Teaching you have learned -  To the "teaching" which you have received in this Epistle and elsewhere; the teaching that these divisions should cease; that the Jewish ceremonies are not binding; that all should lay aside their causes of former difference, and be united in one family; see Rom 14; 15.
(from Barnes' Notes)

Keep away from them - let them have no kiss of charity nor peace, because they strive to make divisions, and thus set the flock of Christ at variance among themselves; and from these divisions, offences (skandala, scandals) are produced; and this is contrary to that doctrine of peace, unity, and brotherly love which you have learned. Look sharply after such that they do you no evil, and avoid them
(Adam Clarke's Commentary)

For such people are not serving our Lord Christ, but their own appetites. - Their own "lusts;" their own private interests; they do this to obtain support. The authors of parties and divisions, in church and state, have this usually in view. It is for the indulgence of some earthly appetite; to obtain function or property; or to gratify the love of dominion.
(from Barnes' Notes)

By smooth talk and flattery - Mild, fair, plausible speeches; with an appearance of great sincerity, and regard for the truth; compare Col 2:4; 2 Peter 3:3. People who cause divisions commonly make great pretensions to peculiar love of truth and orthodoxy; and put on the appearance of great sincerity, sanctity, and humility.
(from Barnes' Notes)

They deceive the minds of naive people - The minds of the unsuspecting, or those who are without guile
(from Barnes' Notes)

The GCLI books (from Great Commission Churches) reads: Yet no matter how wise or sincere or persuasive such people may appear to be, if they
are undermining the truth of the gospel or dividing Christians, even over more minor
issues, they are putting stumbling blocks in the way of God’s people and must be
avoided.
In Titus 3:9-11, Paul commands Titus to avoid “foolish controversies,” “arguments,”
and “quarrels” because they are unprofitable and useless. These quarrels might
be over portions of God’s Word—the Old Testament law. Or they might be over
speculative and peripheral subjects, such as “genealogies.”
Earlier in his letter to Titus, Paul says that there are truths (in context, the truths of the
gospel), that Titus must “encourage and rebuke with all authority” and not let anyone
disregard him (Titus 2:15, NIV). And immediately prior to verse nine, he lays out
truths that are “excellent and profitable for everyone.” Yet people can so easily get
into debates about all kinds of non-important, non-essential issues. Paul says to avoid
such “foolish controversies” because they are “unprofitable and worthless.” They
produce no spiritual benefits and lead to no constructive results.
So division, caused by “heretical” (divisive) people, can occur in the body of Christ
in two ways. The first is when the divisive person undermines the truth of the gospel.
The second is when the divisive person strongly or persistently opposes the “nonessential”
teachings of the leadership of a particular church or movement. Such a
person is failing to acknowledge that God has placed Christians in spiritual families
under the care of spiritual leaders. And although the leaders may not always be
right on every single issue of teaching, if they are preaching the truths of the gospel
accurately, they should not be opposed on more minor issues, at least not opposed to
the point of causing a division. These verses in Romans 16 and Titus 3 can be applied
to either type of divisive person.
The person is to be admonished or reproved for his divisive behavior twice before
we “have nothing to do with him.” This “warning” or “admonition” appears to be an
admonition showing the individual that the divisive teaching or behavior is wrong,
not necessarily a warning that he is about to be rejected from the church.
In other words, if a person’s communication is divisive and he repents after being
admonished, he may remain in fellowship. If he communicates divisively a second
time and repents after a second admonition, he may still remain in fellowship. But if
he communicates divisively a third time, he is to be rejected, no matter how repentant
he may seem. We can be sure that such a person is “warped and sinful.”
In the case of a person who has been divisive and refuses to repent upon being
admonished, it is important to note that the passage says nothing about a time period
being required between admonitions. If, after the first admonition, the person
doesn’t agree that what he is teaching is wrong or divisive, he can be immediately
admonished a second time, even in the same conversation. Thus he can be rejected
immediately if he will not repent and agree to refrain from divisiveness.
Note how much God hates division in His Church! A person could commit other
sins many times and repent each time and still not be the object of church judgment.
But a divisive person is allowed only two verbal repentances before we are to “have
nothing to do with him.” God loves unity and hates disunity among His people.
19. How should a divisive person be treated?
Romans 16:17 says to “keep away from them.” The Greek word translated “keep
away” is “ek-klee`-no” and means to “turn away from, to turn aside, lit., to bend out
of (“ek”, out; “klinoμ”, to bend).” 18
Titus 3:10 says that after a first and second warning, we should “have nothing to do
with him.” The Greek word translated “have nothing to do with him” is “ par-aheeteh`-
om-ahee” and means “to reject or repudiate.” 19
So the divisive person should be “turned away from” and “rejected.” This would
certainly include putting him out of the fellowship as well as instructing the church
not to associate with him. To protect God’s people, it would be wise to inform the
church of the nature of the false teaching or doctrinal hobbyhorse that the person
is promoting and to answer any questions people may have about that teaching.