Browser extensions have emerged as integrated characteristics in modern browsers, with the aim to boost the online browsing experience. Their advantageous position between a user and the Internet endows them with easy access to the user's sensitive data, which has raised mounting privacy concerns from both legislators and extension users. In this work, we propose an end-to-end approach to automatically diagnosing the privacy compliance violations among extensions. It analyzes the compliance of privacy policy versus regulation requirements and their actual privacy-related practices during runtime. This approach can serve the extension users, developers and store operators as an efficient and practical detection mechanism for privacy compliance violations. Our approach utilizes the state-of-the-art language processing model BERT for annotating the policy texts, and a hybrid technique to analyze an extension's source code and runtime behavior. To facilitate the model training, we construct a corpus named PrivAud-100 which contains 100 manually annotated privacy policies. Our large-scale diagnostic evaluation reveals that the vast majority of existing extensions suffer from privacy non-compliance issues. Around 92% of them have at least one violation of either their privacy policies or data collection practices. Based on our findings, we further propose an index to facilitate the filtering and identification of privacy-incompliant extensions with high accuracy (over 90%). Our work should raise the awareness of extension users, service providers, and platform operators, and encourage them to implement solutions toward better privacy compliance. To facilitate future research in this area, we have released our dataset, corpus and analyzer.