I would speculate that Stockholm would keep voting a bit more "right" than the rest of Sweden as long as the "right" consists of parties like the Moderates and Liberals who accept the small "l" liberal consensus among elite opinion (in other words as long as they are the Swedish equivalent of pro-EU Tories in the UK). If we get to a point where the parties of the right in Sweden start to become socially conservative and xenophobic and populist and Eurosceptic etc... then it could create a whole new cleavage and I wonder who would then start to win in Stockholm?
If the Moderates took that path, the Liberals would by definition be the main beneficiaries, it seems to me.