You know what happens when we 'assume'...

I think the irreconcilable difference lies at some very basic assumptions each group makes about life and how people behave as members of society, and the two groups profoundly mistrust one another's underlying assumptions. Conservatives tend to believe in the primacy of the individual, and that the interests of the group will work to the detrement of individual liberty and prosperity. Liberals tend to believe in the primacy of group membership, and that the integrity of society must be protected against unscrupulous individuals. (Soviet-era Communism expands this dynamic of group integrity into group-on-group class warfare, but that has not been the typical experience in the US.)

Of course, ideas are strongly linked to emotion, and our political affiliations can be affected by our attitudes towards people propogating certain ideas as much as by the ideas themselves. And in a two-party system, each platform has so many planks of varying stripes that clear blue/red division is a journalistic convenience, not accurate representation. My politically active youth behind me, I find that there really is no party that represents me any more, and the older I get, the more I'm OK with that.

So my one-liner answer to the question is: it's a matter of trust. Not that they don't trust one another as individuals, but they don't trust the other's underlying philosophies.