When I read this question, an interesting piece of Dutch history immediately sprang to mind: the period 1917-1967. During these fifty years, the Netherlands dealt with a similar problem. Let me explain, and maybe shed some light on this conversation.
The Netherlands has always been a very tolerant country; if you had money, or if you could help others make money, you were more than welcome. This resulted among others in several religious groups living 'together'. Most notably were the Catholics and the non-Catholic Christians (protestants).
At the beginning of the previous century (the 20th), a third group emerged: the socialists. Since one of the dogma's of socialisms is the absence of religion, they were clearly a third group.
These groups stuck together more and more, and finally around 1917 this resulted in what has been called the 'verzuiling', which is probably translated as 'columnization'. Dutch society was not only divided in the usual strata (elite and non-elite) but much more importantly they were divided in columns. Each column had its own elite and non-elite strata and each column minded its own business. Historically, four columns have been identified: the catholic, the protestant, the socialist and the 'neutral' or 'liberal' column. The neutrals thought that columnization was stupid and therefore they are ironically grouped in the fourth column :-)
So far, this does not differ from the American example. Different groups which share a common culture and are not completely happy about the other groups. However, columnization had a historically unique aspect: every column had roughly the same size, the same social status and the same political power.
The media played an important role in the foundations of this columnizations. Every column had its own radio broadcasting corporation and every column had its own newspapers. Furthermore, every column had its own shops, its own clubs and of course its own political party. In short, there were four 'nations' within one nation, all living happily separated from each other.
This meant that e.g. during elections no single party could get the majority. In other words, differing parties had to form a coalition and cooperate. And the elite of every party was more than willing to do so. This prevented many excessive things from happening (since no minority point of view could be accepted), most noteably the fact that there could not be any offical discrimination (apart from the colonial parts of course, but hey, who minded them in those days? :-(
It wasn't until the sixties that the columns grew back together again. WW2 started this process ("we're all dutch against the others") but it was the western-worldwide culture change which meant the 'end' of the columns.
The results are still visible. In the Netherlands we still have loads of political parties and media companies (even though my generation is not quite sure which company has which beliefs :-), coalitions of two or three parties with oppositions of four of five parties have reigned as long as I can remember, and cooperation is an essential part of dutch politics. There is hardly any resistance to the formation of new 'special' schools, like muslim schools. All in all, I think I live in a pretty tolerant country nowadays.
So, how does this all relate to your question? I think this example shows that this 'my culture, my heritage' thing can eventually result in good things, provided that there are multiple parties with equal social/economic/political powers. Unfortunately, I do not have the impression that this is currently the case in America.
But I believe (or hope :-) that this will change. I'm not quite sure of the demographic numbers, but AFAIK black people and hispanic people already form a large population in the US. If only they were to have their own political parties, a lot of discrimination would disappear. (Note, with discrimination I mean giving some parties less rights than other parties. I think that 'thought-discrimination' will never disappear).
Just some food for thought.