Contact tracing has emerged as one of the main mitigation strategies to prevent the spread of pandemics such as COVID-19. Recently, several efforts have been initiated to track individuals, their movements, and interactions using technologies, e.g., Bluetooth beacons, cellular data records, and smartphone applications. Such solutions are often intrusive, potentially violating individual privacy rights and are often subject to regulations (e.g., GDPR and CCPR) that mandate the need for opt-in policies to gather and use personal information. In this paper, we introduce Quest, a system that empowers organizations to observe individuals and spaces to implement policies for social distancing and contact tracing using WiFi connectivity data in a passive and privacy-preserving manner. The goal is to ensure the safety of employees and occupants at an organization, while protecting the privacy of all parties. Quest incorporates computationally- and information-theoretically-secure protocols that prevent adversaries from gaining knowledge of an individual's location history (based on WiFi data); it includes support for accurately identifying users who were in the vicinity of a confirmed patient, and then informing them via opt-in mechanisms. Quest supports a range of privacy-enabled applications to ensure adherence to social distancing, monitor the flow of people through spaces, identify potentially impacted regions, and raise exposure alerts. We describe the architecture, design choices, and implementation of the proposed security/privacy techniques in Quest. We, also, validate the practicality of Quest and evaluate it thoroughly via an actual campus-scale deployment at UC Irvine over a very large dataset of over 50M tuples.