The digital era has raised many societal challenges, including ICT's rising energy consumption and protecting privacy of personal data processing. This paper considers both aspects in relation to machine learning accuracy in an interdisciplinary exploration. We first present a method to measure the effects of privacy-enhancing techniques on data utility and energy consumption. The environmental-privacy-accuracy trade-offs are discovered through an experimental set-up. We subsequently take a storytelling approach to translate these technical findings to experts in non-ICT fields. We draft two examples for a governmental and auditing setting to contextualise our results. Ultimately, users face the task of optimising their data processing operations in a trade-off between energy, privacy, and accuracy considerations where the impact of their decisions is context-sensitive.