Visual navigation is a fundamental capability of mobile service robots, yet the onboard cameras required for such navigation can capture privacy-sensitive information and raise user privacy concerns. Existing approaches to privacy-preserving navigation-oriented visual perception have largely been driven by technical considerations, with limited grounding in user privacy preferences. In this work, we propose a user-centered approach to designing privacy-preserving visual perception for robot navigation. To investigate how user privacy preferences can inform such design, we conducted two user studies. The results show that users prefer privacy-preserving visual abstractions and capture-time low-resolution preservation mechanisms: their preferred RGB resolution depends both on the desired privacy level and robot proximity during navigation. Based on these findings, we further derive a user-configurable distance-to-resolution privacy policy for privacy-preserving robot visual navigation.