Wow. Firstly, if you're interested in Jewishness, you should take a class in a Jewish Studies department (I believe coursera has some if you're not within reach of a university), because I would have to write a book to address all of your issues. Secondly, these are some thought-provoking questions, but some of them are grounded in a fundamental misunderstanding of Judaism, Jewishness, and identity. So let's lay out the facts first.

Judaism is a religion grounded in tribalism. It is different from other religions because it is not expansionary - Judaism discourages conversion. The Jewish people are a kind of family (well, literally a family - they are all in theory descended from one patriarch, Abraham), and their bond is not only a shared belief system, but also blood. What many Gentiles don't know is that the Jewish people are also a landed people - they are not nomads, like the Romani or the Samoed, but a displaced people that still maintains a strong spiritual bond to the Land of Israel, which is cultivated through both Jewish religion and Jewish culture. In modernist parlance, the Jewish people are a nation. But because many Jews live in diaspora, it is difficult to accommodate their identity in the same legal, geopolitical way that we accommodate the Germans, Italians, or Americans. We will get to Israel in a second, but one could argue that, even despite Israel (which is the nation-state of the Jewish people), diaspora is a huge part of the Jewish identity as well.

Your ideas about the fluidity and divisiveness of identity are not new - ever since the Enlightenment, your ideas were held by many educated European Jews (if you are interested, The Jewish Century by Yuri Slezkine discusses this issue). Many Jews believed that, if they shed their old Jewish customs, became educated in the ways of their host countries, and became "natively" German, Italian, Russian, whatever, then they would become citizens of the world and stop being Jewish, to the benefit of everyone. In some European countries, their strategies were not successful because these countries were antisemitic. However, even in enlightened places like Germany or England, the Jews were singled out as Other, denied the rights of their fellow citizens, even though they dressed, spoke, and lived exactly like the locals (the founder of UCL was famously expelled from Cambridge when he refused to be Christened in order to attend, which led to the founding of UCL; and of course we all know what happened in Germany). To be clear, the modern paradigm (Enlightenment values, secularism, individualism, liberalism, democracy - and also communism) promised equality between all people, even the Jews, but when the Jews of Europe believed in that, it backfired on them in a really big way. There was some mistrust by the Jews of "civilized Europe" from then on, which is masterfully discussed in Zygmunt Bauman's Modernity and the Holocaust.

Israel. One of the perhaps paradoxical currents of modernity was nationalism: big empires crumbled into small states of people that wanted to live by their own culture and philosophy, rather than adopting that of the Austrians or English or Russians, and small city-states banded into countries in order to be more effective bargainers on the global stage. There emerged the belief that the Jews too should have their own state, which is called Zionism (you can read Theodor Herzl's Altneuland ], which is the sort of Torah of Zionism). The reasoning for that is that states are divided on the basis of nationhood - they are nation-states. To be clear, Canada, Australia, and the US are special cases, because they are countries founded by immigrants, and nationality there is conferred on the basis of jus soli, i.e. if you are born in that country, you receive that country's nationality. Most countries in Europe are jus sangui, i.e. one or both your parents have to be nationals of that country in order for you to obtain citizenship. There are historical reasons for that: back when the Europeans were dividing up their lands, a country's claim to a piece of land came from the argument that the people who lived on that land were culturally, linguistically, whatever different from the other people who surrounded them, and that made them a nation, and a nation deserves land. This is important for the Jews because the Jews were considered foreigners (and still are). Whilst some Jews believed that, by shedding their Jewish identity, they would become locals, others believed that the Jews would never be accepted as equals by the Europeans, so they came up with various plans to build a homeland for the Jews (in Argentina, Israel, Russia, etc). To some degree, there is a consensus that this latter group was right.

Now to your issues. I can't address all of them, so I will address the ones that are most interesting to me.

When the members of nation share a common identity that is inclusive, it allows for cohesion and cooperation.

I can understand why a Canadian or American would think so, but the rest of the world doesn't work like that. Most nation-state identities are not inclusive even today. There is an expectation that, for instance, in order to be "truly British", one must not only speak English, but dress a certain way, be baptized into a certain religion, and have a certain skin color; this expectation does not exist in Canada. Identities run deeper than you think.

Secondly, why do you think that national identities are any more inclusive than clan identities? As an immigrant, I do not feel included in my host country. I am banned from some major aspects of civilian life. Why are people's rights determined by what passport they have, rather than by something more efficient - such as how much education they have, how they can practically contribute to society, or how disease-free they are? We don't have national identities because they're the best thing that's ever happened - national identities are just as much an ideology, often a backward ideology, as tribal ones.

We shouldn't care about identities beyond what is necessary to function and communicate.

It's nice that you think that, but social phenomena don't operate according to how you believe they should. Identities, fundamentally, are simply the communal patterns in which people have been raised: somebody who grew up in a conservative community will have a conservative identity (which they can reject), somebody who grew up in New York a New York identity, somebody who spoke Spanish a Spanish-speaking identity. Those are just things that people are, that form them into groups that are sometimes cohesive and sometimes not. You don't get to decide - none of us get to decide - how a society categorizes itself.

An obsession with maintaining the Jewish identity can make other people feel left out

This is silly. Do you feel left out by gay bars? Do you feel left out by books written in a foreign language? Do you feel left out by women's bathrooms? Some things we are, and some things we are not, and some we can never be - this is a fact of life. Why do you want to deny this by "including everyone"? There is nothing wrong with having a space for a certain identity, whatever it is, as long as that identity doesn't take over all the space. People of similar identities often go through similar experiences, and they need those spaces to share those experiences. Think of something you couldn't share with a member of the opposite sex, somebody from a different country or generation. Is it wrong to seek likeminded people whom you will be able to share that with? Like I said, I'm an immigrant, and people who are not immigrants simply haven't gone through the things I have, and they don't have the information I need, so I sometimes specifically hang out with people like myself. You wouldn't fit in our company - you'd be bored. But is you being bored a reason for me not to do my thing?

I doubt anybody's read this far, but if you have, thank you, and I will gladly field any questions.