The world's power systems are undergoing a rapid transformation, shifting away from carbon-intensive power generation to renewable sources. As a result, electricity is being transported over ever longer distances, while the intrinsic system inertia provided by thermal power plants decreases. Together, these developments raise the probability of cascading line failures and reduce the stability of the system after a system split. In this article, we assess the risk of cascading failures and system splits in the European power grid for different carbon reduction scenarios. We analyze the most likely and most dangerous splits, and identify critical transmission infrastructures and we discuss potential countermeasures that can address the problem of cascades. Our results show that while the risks of splits causing power failures rises with decarbonization, it can be mitigated cost efficiently.