East is East and West is West and never shall the twain meet

No, Kipling, I disagree. Profoundly.

Firstly, East and West are really quite arbitrary labels.
Consider that for most of our existence, we Chinese have described ourselves as the Centre, and everyone else as the periphery, or, to put it more bluntly, as barbarians. Before you start caterwauling about how unkind this is, note that the Romans indulged in more or less the same sort of name-calling when they labeled everyone living outside their borders barbari. We might as well have labelled ourselves the West and Europe the East -- if, starting from China, you go all the way East across the Pacific, across America, and then across the Atlantic, you do get to Europe, no? The point is, these labels are entirely arbitrary. They could very well refer to different things than they actually do, but for some accidents of history.
The labels are not only arbitrary, they are also shifting. For the forty-five years or so after the defeat of Nazi Germany by the Allies, when two of the Allies engaged in a crazed, frenzied staring match involving elaborate taunts, 'East' was appropriated to refer to one of the Allies and her friends, and 'West' restricted to refer to the opposing camp.
Even when these labels weren't being fitted to politically-motivated purposes, their meanings still change over time, as the horizons of human knowledge change. At first the emphasis of "East" was on the Islamic (and perhaps pre-Islamic) civilisations of the Middle East; then it shifted further East, to India and China. All of these perhaps share some common differences compared to the Judo-Graeco-Roman cultures of Europe, but they also have some substantial differences between themselves. With each subtle shift in meaning of the increasingly broad umbrella term "East", the underlying contrasts the labels are meant to bring out becomes increasingly general and vague and possibly, just, unclear.
So it just does not cut it to state, this baldly, that 'East is East and West is West.'

Secondly, and more importantly, cultures are not static, undying, eternal stone monuments. They evolve over time, sometimes with startling rapidity. They adapt to the emergence of new technologies and phenomena, communicate with and influence one another, and generally do not stay still. As countries Eastern and Western alike become industralised, and globalisation creates a continuous dialogue between East and West, the twain are not only meeting, but increasingly fusing to form a composite entity.

The general differences between the civilisations of Asia and those of Europe that might have, in the past, led people like Kipling to distinguish so ardently between "East" and "West", I propose, are really, above all, results of social and economic circumstances, governed largely by geography and historical evolution. They are not inexorable realities or signs of a mysteriously-ordained order. As these social and economic circumstances change around the world, so we see that these differences are no longer the same ones, or perhaps that they have narrowed and may disappear altogether.