The lack of modularity in synthetic biology presents one of the major bottlenecks in the scalability of complex gene circuits. One source of this context-dependent behavior is the scarcity of shared transcriptional and translational resources. To overcome this issue, predictive computational tools must account for the resulting competition phenomenon both when studying individual cells and at the population-level considering cell-to-cell heterogeneity. Since toggle switches are one of the most widely used genetic modules, here we focus on how shared resources affect the stability profile of toggle switches even in the presence of loading from their context. Modeling the parameters of the toggle switch as random variables reveals how cellular context, noise and correlation between key parameters shape the population-level stability distribution. To demonstrate the relevance of our results, we illustrate that detrimental effects of even unknown contexts can be bounded, thus enabling the design of genetic modules that are robust to disturbances due to unknown loading effects.