If the postal service would be that important in the eyes of the Danish and Swedish governments, then they wouldn't have re-structured their postal services as

If the postal service would be that important in the eyes of the Danish and Swedish governments, then they wouldn't have re-structured their postal services as a state owned company, but kept it a state agency. But they didn't. In turn the postal workers are no longer state officials, which comes with a loss of job security, but instead they gained the right to strike. You can petition the government to undo this semi-privatization of course. Strikes are regulated in Denmark and Sweden, and usually need to be organized by a proper union, and can be deemed unjustified by a court - like it happened in this case, until that decision was overturned again. This makes your fears of "socially conservative" "unions" unlikely. :)