Forests provide important ecosystem services (ESs), including climate change mitigation, local climate regulation, habitat for biodiversity, wood and non-wood products, energy, and recreation. Simultaneously, forests are increasingly affected by climate change and need to be adapted to future environmental conditions. Current legislation, including the European Union (EU) Biodiversity Strategy, EU Forest Strategy, and national laws, aims to protect forest landscapes, enhance ESs, adapt forests to climate change, and leverage forest products for climate change mitigation and the bioeconomy. However, reconciling all these competing demands poses a tremendous task for policymakers, forest managers, conservation agencies, and other stakeholders, especially given the uncertainty associated with future climate impacts. Here, we used process-based ecosystem modeling and robust multi-criteria optimization to develop forest management portfolios that provide multiple ESs across a wide range of climate scenarios. We included constraints to strictly protect 10% of Europe's land area and to provide stable harvest levels under every climate scenario. The optimization showed only limited options to improve ES provision within these constraints. Consequently, management portfolios suffered from low diversity, which contradicts the goal of multi-functionality and exposes regions to significant risk due to a lack of risk diversification. Additionally, certain regions, especially those in the north, would need to prioritize timber provision to compensate for reduced harvests elsewhere. This conflicts with EU LULUCF targets for increased forest carbon sinks in all member states and prevents an equal distribution of strictly protected areas, introducing a bias as to which forest ecosystems are more protected than others. Thus, coordinated strategies at the European level are imperative to address these challenges effectively. We suggest that the implementation of the EU Biodiversity Strategy, EU Forest Strategy, and targets for forest carbon sinks require complementary measures to alleviate the conflicting demands on forests.