The rapid advancement of diffusion models and personalization techniques has made it possible to recreate individual portraits from just a few publicly available images. While such capabilities empower various creative applications, they also introduce serious privacy concerns, as adversaries can exploit them to generate highly realistic impersonations. To counter these threats, anti-personalization methods have been proposed, which add adversarial perturbations to published images to disrupt the training of personalization models. However, existing approaches largely overlook the intrinsic multi-image nature of personalization and instead adopt a naive strategy of applying perturbations independently, as commonly done in single-image settings. This neglects the opportunity to leverage inter-image relationships for stronger privacy protection. Therefore, we advocate for a group-level perspective on privacy protection against personalization. Specifically, we introduce Cross-image Anti-Personalization (CAP), a novel framework that enhances resistance to personalization by enforcing style consistency across perturbed images. Furthermore, we develop a dynamic ratio adjustment strategy that adaptively balances the impact of the consistency loss throughout the attack iterations. Extensive experiments on the classical CelebHQ and VGGFace2 benchmarks show that CAP substantially improves existing methods.