BUDAPEST—A surge in price growth in eastern Europe has opened a rift between central banks that have launched rate hikes to battle inflation and populist governments trying to defend a strong economic recovery. The standoff is most apparent in Hungary and the Czech Republic, where national elections have complicated the task of central banks, which have led the way in the European Union in monetary tightening. Both have raised their key rates by more than a percentage point since June. Tight labor markets and expansionary fiscal policies have added to global pressures on inflation, which economists say could haunt the EU’s east longer than initially believed. “Central and Eastern Europe is one of the regions of the world where we think that the risk of sustained higher inflation in the next few years is greatest,” Capital Economics analyst Liam Peach said. Facing the prospect of a close election next year …