Planning under deep uncertainty, when probabilistic characterizations of the future are unknown, is a major challenge in water resources management. Many planning frameworks advocate for "scenario-neutral" analyses in which alternative policies are evaluated over plausible future scenarios with no assessment of their likelihoods. Instead, these frameworks use sensitivity analysis to discover which uncertain factors have the greatest influence on performance. This knowledge can be used to design monitoring programs and adaptive policies that respond to changes in the critical uncertainties. However, scenario-neutral analyses make implicit assumptions about the range and independence of the uncertain factors that may not be consistent with the coupled human-hydrologic processes influencing the system. These assumptions could influence which factors are found to be most important and which policies are most robust, belying their neutrality; assuming uniformity and independence could have decision-relevant implications. This study illustrates these implications using a multistakeholder planning problem within the Colorado River Basin, where hundreds of rights holders vie for the river's limited water under the law of prior appropriation. Variance-based sensitivity analyses are performed to assess users' vulnerabilities to changing hydrologic conditions using four experimental designs: (1) scenario-neutral samples of hydrologic factors, centered on recent historical conditions, (2) scenarios informed by climate projections, (3) scenarios informed by paleohydrologic reconstructions, and (4) scenario-neutral samples of hydrologic factors spanning all previous experimental designs. Differences in sensitivities and user robustness rankings across the experiments illustrate the challenges of inferring the most consequential drivers of vulnerabilities to design effective monitoring programs and robust management policies.Plain Language Summary How we should best manage our water resources depends on future water supply and demand, both of which are changing in uncertain ways as a consequence of climate change, population growth, and sectoral change. This makes it challenging to decide between alternative management plans that may be most favorable under different conditions. Given this uncertainty, many planning frameworks advocate for implementing "robust" management plans that perform reasonably well over a wide range of conditions. These plans can then be modified adaptively to cater to particular climate and socioeconomic conditions as our uncertainty about the future is reduced. Unfortunately, we find that the determination of which plan is most robust, and what conditions should trigger adaptation, is an additional challenge. In assessing the vulnerabilities of hundreds of water users in the Upper Colorado River Basin to different possible drought conditions, we find different users to be robust depending on which scenarios are considered. The sensitivities of these users' water shortages to different climate conditio...