I would say I would draw the "Yes, definitely" line at cultural nationblocks. That isn't to say that other consistently divergent areas without the cultural impetus shouldn't also be independent (though figuring out a name less bland than "Northwest England" for example is a factor ;P), just it needs to be considered a mite more thoughtfully. Such as, is such an area wildly divergent, or just a little bit? Like the difference between Democrat/Republicans versus the difference between hardline socialists and neo-liberalism.
Another factor is would such a place be able to sustain itself? Being politically represented is nice, but not if it comes at the price of a functional economy. If your area hemorrhages people who seek a better life elsewhere (and thereby lose whatever political representation such independence would have gained them), then what's the point?
Another is political homogeneity. It wouldn't do to have a patchwork of villages and cities in one country, and cities and villages literally next door and between them in another country. Like trying to give the Jews a country, by taking all the Jewish-majority areas in cities across the world and giving those cities and city-quarters to a Jewish state. It wouldn't work. Of course, that's an absurd example, but you get my idea. A better example would be the democrat/republican divide. There is the south/north divide, but you also have rural areas that are more republican in the north, and urban areas that are more democrat in the south. A true split along those lines would be a patchwork.
Also, depending on HOW divergent the opinions are, devolution and confederacy is probably a better bet than outright independence. Political consensus rather than exile of the other party, from either perspective.