The differerences that would prevent a Nordic union are not cultural but political, mainly to do with foreign political and economic interests. Norway in this time period was oriented towards the West, traditionally being a fishing and sea trade nation, and thus will in the first decades of the 20th century see its interests aligning with Britain and her allies. Sweden was traditionally neutral since the 19th century and was very wary of getting into entangling alliances, sitting right between Britain, Germany and Russia. Finland, if it gains independence, would first of all be concerned with not being retaken by the Russians, and if threatened, would ally with anyone who promises it support against the East - from anyone who is positioned as Russia's geopolitical rival or enemy, that is.
So - in pretty much any scenario where the major powers of Europe find themselves at war against each other, these three Nordic nations would see their interests clash. As the politicians in each nation could see this also beforehand, in theory, it provides a simple rationale why putting an union together would be difficult. The main snag I can see is that Sweden, as the biggest nation, would have to be the prime mover in pushing for such a union, but then it is easy to understand that in this union, Stockholm would have to militarily guarantee Norway and Finland. That, especially for Finland and its relations with Russia, would be a very serious problem for upholding Swedish neutrality in any future conflicts.
