Replacing conventional generation with inverter-interfaced units has turned distribution networks (DNs) from consumers to active and responding intelligent DNs. These modern DNs contain several devices that can support the transmission network (TN) and system stability. Typically, deterministic and aggregated models for inverter-interfaced generation and conventional loads are used to include entire DNs in bulk system stability studies, and contributions from smart loads are neglected. This approach introduces errors to the dynamic modeling that can lead to instabilities. In this paper, we first present a full detailed model of a modern DN, enhancing existing thermal load and distributed generation models to include frequency and voltage support and protection functions required in low-inertia systems. Then, we incorporate the uncertainty that stems from the parameterization of such units using a Monte-Carlo method. Finally, we assess the impact of neglecting specific protection and support functions against frequency disturbances. The results show the crucial importance of accurately modeling protection and support functions to analyze the impact of modern DNs on bulk system stability. In addition, the findings highlight the increased relevance of considering uncertainty in stability studies of weak and low-inertia power systems.