Integrated sensing and communication (ISAC) enables intelligent wireless infrastructure but raises growing regulatory concern as fine-grained personal trajectory histories become a byproduct of sensing. General Data Protection Regulation (GDPR) Articles 5(1)(c) and 5(1)(f) require that personal data be limited to what is necessary and protected through appropriate technical measures against unauthorised reconstruction. This paper addresses both requirements through a Fisher information density (FID)-constrained trajectory sharing scheme for robot collision avoidance, where sensing estimates are perturbed according to local information content before sharing. Experiments on real pedestrian traces show that FID-controlled sharing achieves a strictly better privacy-utility tradeoff than fixed-error perturbation: at matched missed-conflict rates, reconstruction leakage and sustained exposure lengths are consistently lower, establishing information-aware perturbation as a principled technical measure aligned with GDPR data minimisation and integrity requirements.