While there is a truth to what you are saying, this kind of rhetoric really doesn't lead us anywhere.  If the spectrum is a circle, while one may place one's hope in that one particular point where the labels melt away, there are all the other points along that circle.  In the end, one has this desire point, and everything that is not the desired point, and we have another dichotomy.  One can see much of the history of honest political debate about what constitutes that desired point on the circle - the place those who would open their eyes to the truth in the world and in their heart would easily see as the obvious. 

Of course, we should call for the seeking of common ground.  Yet I would ask who is that you want to fight, once united.  What constitutes membership in the "Them" or the "Not Us United" group?  What constitutes membership in the "We."  Around what is everyone uniting? Seems we have more dichotomies.

The quest is not to achieve a dichotomy-free existence, because such an existence is impossible.

As long as the mind keeps silent in the motionless world of its hopes, everything is reflected and arranged in the unity of its nostalgia. But with its first move, the world cracks and tumbles: an infinite number of shimmering fragments is offered to its understanding.

- Albert Camus

The human mind, attempting to understand the world, views the world through dichotomies - one of the most key ones: I/not-I.  Wherever people find themselves on the circular political spectrum is an outcome of how they have come to understand, arrange and prioritize (hierarchicalize) fundamental dichotomies.

We can think of ourselves as one people, but when conflict arises over scarce resources such as, say, water, then other dichotomies arise, such as those of my family/those not of my family, those not of my country/those not of my country, and so on. 

In order to resolve these conflicts, set policies, develop strategies, implement solutions, we face the need to develop dichotomies in order to communicate with each other.  Some of these, like conservative/liberal (or conservative/not-conservative, liberal/not-liberal) while serving a purpose can also lead to being manipulated by some seeking their agenda.  This is part because the nature of any dichotomy is a lacking in specificity for it is a construct of the mind refusing to remain motionless.

Stand and Fight.

The "false dichotomies" you reference also make that call to arms . If you would reject their terms describing what conflict is happening right now, then something more than saying they are all arbitrary is required if you would call others to your side to fight with you. If you are writing as a parodist, the device is perfect. You might be saying: "this is what a call to arms sounds like."

But if you are sincere, the language just doesn't work. There is no actual concept being introduced. It is only a protest being raised faintly against other protests.

The video starts with a Krishnamurti quote. His path was unique and I have no interest in establishing how much or little he "knew." But I have long been attracted to the way he calls for us to "think for ourselves." Where is the battle cry in that appeal?

I went to the side bar and looked for an appropriate place to insert this comment. It is is not related directly to any continuance of my thoughts about this blog when it was getting a bit of discussion, but I think it is a good fit. It is about David Frum.
 First, when Frum was becoming known to me through his association with, and service for, the Bush administration, the mildest sort of direct interaction I could wish to have with him was to hit him in the face with a cow patty. He still deserves it for what he did then, IMO.  
 
 I recommend a video conversation on Bloggingheads TV between Robert Wright and David Frum. Not to try to make anyone a fan of Frum, I hope everyone keeps a cow patty handy for him any time he tries to mitigate or apologize for his previous role. He does a bit of that, IMO,and in the context of the rest of his presentation it is a bit ironic. But, the conversation, centered around his new book, while revealing  nothing that isn't widely known or believed already by many informed people, is one I found very interesting and very topical in relation to some  of our country's most pressing problems.
 I hope the video blog gets a very wide viewing and I [expect] I will be happy if his book is wildly successful, though I doubt either will happen. If I had to choose only one side of the political spectrum to listen to him in this interview and to read him, I would choose for the Republicans to be the ones, and I would hope they gave some open minded thought to what he is saying. Who he is, and who he has been, is an important part of the context. I commend Wright for his handling of this interview.
 The blog is 46 minutes long and I think worth listening to in its entirety from front to ending for anyone with the time and inclination,  just like it is the best way to read a book, but there are a number of topic headings that can be clicked on for a shorter sampling. 

http://bloggingheads.tv/videos/9689