VR empirical data include the sensitive affective and behavioral data (e.g. gaze patterns, physiological signals, facial expressions), placing a person at the risk of re-identification. Tailored privacy-preserving approaches to immersive data have not, however, received much attention in the recent affective-computing investigations. In the present paper, a differentially-privacy (DP) framework is presented as that allows anonymizing VR-based studies of emotion without losing scientific value. The first one is the quantification of re-identification risks through empirical linkage and inference attacks and then the mitigation of the risk through DP mechanisms such as Laplace noise, that sought to reduce the re-identification risks by 80%. At the same time, the strategy returned an 85% retention with respect to utility relating to emotion-classification. The results can allow sharing VR-collected affective data safely to use in research without infringing GDPR/HIPAA provisions and thus offer practical procedures in implementing DP in VR-based empathy research and developing ethical data collection practices in the field. Finally, on the one hand, the framework mediates between immersive technology and information privacy, and on the other hand, it enables the development of emotional AI and psychological research by providing anonymity of the participants. Among its contributions, VR-specific parameter optimizations and a risk-utility assessment metric, there are specific findings towards the higher priority of effectiveness of affective datasets in the VR-based therapy and social-emotional learning.