Hydrogen is called to be one of the main energy vectors in future energy systems, especially for energy storage, where this carrier presents some interesting features. Its application in microgrids might help to improve economic, environmental and reliability indicators, providing greater storage capacity than other technologies, like batteries. Following this idea, this paper develops a robust energy management methodology for isolated microgrids considering hydrogen storage and demand response initiatives. The new proposal is raised as a nested max-min optimization framework. To reduce the original problem to a tractable single-level one, a master-slave scheme is developed by which binary variables can be fixed and thus the inner problem can be reduced to its equivalent Karush-Kuhn-Tucker conditions. Then, the overall optimization paradigm is solved in an iterative fashion used the Constraint-and-Column Generation Algorithm. The resulting tool is applied to a benchmark isolated microgrid, thus validating it for industry applications. Moreover, different relevant results are analysed in-depth. Thus, the role of hydrogen storage and demand response initiatives is discussed, concluding that flexible demand has a more notable impact on monetary savings than hydrogen storage, reducing the total cost by 6 % with respect to the base case. Some intrinsic issues are also identified. For example, it is observed that flexible consumers are more frequently called when the hydrogen chain is enabled, which may provoke undesirable effects like response fatigue.