Is there a biblical basis for the division caused by theology? Is there a Biblical basis for the division caused by various theologies?

Let us take James into account:


  James 1:26-27 
  If any man among you seem to be religious, and bridleth not his tongue, but deceiveth his own heart, this man's religion is vain. 
  Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world. 


As well as Paul:


  1 Corinthians 1:10
  Now I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment. 


In reading these, I'm sure we can all agree that we are, in fact, not doing either of these at all. We have Catholics, Lutherans, Mormons, JWs, and many many more - all doing and saying and teaching different things. This becomes problematic for some people who are trying to learn the Truth (emphasis on that capital T), and many people incredibly devoted to what is (or appears to be, rather) wrong will quote such verses as 1 Corinthians 14:33 - however you will find someone do this, then immediately go and contradict Scripture itself.

There are many, many denominations out there - and I'm sure an equal or greater amount of theologies. And if my usage of the term theology appears off, that's because theology today does not do what it was supposed to. Instead of studying God, much of it (from personal observation) is finding out "what the book means to you". God did not inspire the Bible to appeal to each individual, but to His people.

So, is there a Biblical basis for the division it is causing?
INTRODUCTION

Your specific question is not overly clear, but it seems you are essentially asking if there is any doctrine worth dividing over, and you mention the many denominations that exist as problematic.  

I'm reminded of the satirical quote by Steve Turner:

We believe that all religions are basically the same, at least the one we read was.     
They all believe in love and goodness, they only differ on matters of creation, sin, 
heaven, hell, God, and salvation.


In short, yes, there are doctrinal differences worth dividing over, and there is, indeed, a biblical basis for this.  Yet, there are also doctrinal differences that are not worth dividing over as well.

An old axiom is instructive at this point:

In Essentials Unity, 
In Non-Essentials Liberty, 
In All Things Charity.


So, we have to determine what are the essentials and what are the non-essentials.  People will differ on this, but the essentials should probably include 1) the nature of God and 2) the doctrine of salvation at the very least.

ESSENTIALS

Paul wrote his letter to the Galatians to specifically correct heretical doctrine, and he uses some pretty strong language to do so.


  I am amazed that you are so quickly deserting Him who called you by the grace of Christ, for a different gospel; 7 which is really not another; only there are some who are disturbing you and want to distort the gospel of Christ.  Galatians 1:6-7 NASB


Paul continues with strong words against those that had perverted the purity of the gospel:


  But even if we, or an angel from heaven, should preach to you a gospel contrary to what we have preached to you, he is to be accursed! 9 As we have said before, so I say again now, if any man is preaching to you a gospel contrary to what you received, he is to be accursed!  Galatians 1:8-9 NASB


Thus, the purity of the gospel of grace is, indeed, worth dividing over.  Paul preached salvation by grace and not of works and was willing to divide with those who preached a salvation based on law.

NON-ESSENTIALS

Non-essential issues include many things, including church order, musical preference, the use of certain spiritual gifts and other things.  Here in America, we have the luxury of going to the particular church that best aligns with all of our individual idiosyncrasies and personal preferences, yet in many other parts of the world, much more unity is displayed, particularly in places where Christianity is under persecution.  Still, most mature Christians maintain healthy fellowship and unity with those with whom they differ in non-essentials.

CONCLUSION

So, yes, if someone distorts the nature of God or the doctrine of salvation, we should follow the example of Paul and divide over that.  Draw the line in the sand and do not compromise.

Yet, for many other things, we in the West can choose to gather in different buildings and segregate based on peculiar non-essential issues, but we should certainly maintain unity in the faith with all our brothers with whom we can unite in the essentials.