I don't think you ever hear a conservative make a call for dropping ideological labels.
Call's for unity are nonsensical because it is in an essence asking the opposition to drop their objections, and jump on board your sound, logical, and objective bandwagon.
http://www.constitution.org/wj/meow.htm
William James and other progressives have pushed that we can have a moral equivalent of war, the idea is that - if we can have a war other then actual war, that we can get people to rally around the state, to get people to drop their individual pursuits, to drop their free associations.
The conservative opinion is that all of these in one way or another are just more ways for the state to claim authority over another aspect of life. You have to behave as if we are in a war, we are being invaded by a common enemy. Climate change is one, there's the war on drugs, heterosexual aids is another, there's the war on smoking. (The war on terror doesn't count because that's an actual war, the war on drugs qualifies domestically though.)
Whether these issues are real or valid is not the point, they are wars in which is sold as affecting everyone, and require us to drop our free associations and our ideological labels so that we can all unite and move forward with pragmatic and constructive action.
That is the reason we keep ideological labels is because we actually believe in the things we stand behind. Make the case for us dropping these associations to unite behind some issue, and if it is a good case that appeals to the oppositions values and beliefs, then we'll join.
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