Brian Kennedy, A Passion to Oppose: John Anderson, Philosopher, Melbourne University Press, 1995, p. 141:
Melbourne intellectuals came to regard [John] Anderson 'as the man who had betrayed the Left, a man who had gone over to the other side. Melburnians wanted Anderson to answer a simple question: was he or was he not interested in the fact that some were very rich and some were very poor?' To this question Anderson replied that 'we are all bothered by different things. That finished him with the Melburnians'. [Kennedy quotes Manning Clark, The Quest for Grace, Melbourne, 1991, p. 193]
"We are all bothered by different things." And even when we are bothered by the same things, we prioritize the objects of botherment differently. Now suppose you and I are bothered by exactly the same things in exactly the same order. There is still room for disagreement and possibly even bitter contention: we are bothered to different degrees by the things that bother us.
"It angers me that that doesn't anger you!" "It angers me that you are insufficiently angered by what angers both of us."
Here then is one root of political disagreement. It is a deep root, perhaps ineradicable. And it is a root of other sorts of disagreement as well. We are bothered by different things.
Are conservatives bothered by gun violence? Yes, of course. But they are bothered more by the violation of the Second Amendment rights of law-abiding citizens. Liberals, even if they are slightly bothered by the violation of these rights, assuming they admit them in the first place, are much more bothered by gun violence. Now there are factual questions here concerning which agreement is in principle possible, though exceedingly unlikely. For example there is the question whether more guns in the hands of citizens leads to less crime. That is a factual question, but one that is not going to be resolved to the satisfaction of all. Conservatives and liberals disagree about the facts. Each side sees the other as having its own 'facts.'
But deeper than facts lie values. Here the problem becomes truly intractable. We are bothered by different things because we differ about values and their ordering. Conservatives and presumably most liberals value self-reliance but conservatives locate it much higher up in the axiological hierarchy. This probably explains why liberals are more inclined to rely on professional law enforcement for protection against the criminal element even while they bash cops as a bunch of racists eager to hunt down and murder "unarmed black teenagers" such as Michael Brown of Ferguson fame.
As for what finished Anderson with the Melburnians, he was apparently not sufficiently exercised by (material) inequality for the tastes of the latter despite his being a man of the Left, though not reliably so due to his iconoclasm.
Does it bother conservatives that there is wealth inequality? To some extent. But for a(n American) conservative liberty trumps equality in the scale of values. With liberals it is the other way around. Liberals of course cherish their brand of rights and liberties and will go to absurd extremes in defending them even when the right to free expression, a big deal with them, spills over into incitement to violence and includes the pollution of the culture with pornography. Of course, this extremism in defense of free expression bangs up against the liberals' own self-imposed limit of political correctness. The trashers of Christianity suddenly become chickenshits when it comes to the trashing of Islam. That takes more courage than they command. And they are easily cowed by events such as the recent terrorist attack on Charlie Hebdo in Paris. Liberals are also absurdly eager to spread the right to vote even at the expense of making the polling places safe for voter fraud. How else do you explain their mindless opposition to photo ID? But not a peep from liberals about 'real' liberties and rights such as gun rights, the right to private property, and the right to freedom from excessive and punitive taxation.
Is material inequality a problem? Not as such. Why should it be?
As I recall John Rawls' Difference Principle, the gist of it is this: Social and economic inequality is justified ONLY IF the inequality makes the worse off better than they would have been without the inequality. Why exactly? If I'm smarter than you, work harder, practice the ancient virtues, avoid the vices, while you are a slacker and a screw-up who nevertheless has what he needs, why is my having more justified ONLY IF it makes you better off than you would have been without the inequality? (Yes, I know all about the Original Position and the Veil of Ignorance, but I don't consider that an argument.)
At the root of our difference are value differences and those, at bottom, are irreconcilable.