Reproducible container builds promise a simple integrity check for software supply chains: rebuild an image from its Dockerfile and compare hashes. We build a Docker measurement pipeline and apply it to a stratified sample of 2,000 GitHub repositories that contained a Dockerfile. We found that only 56% produce any buildable image, and just 2.7% of those are bitwise reproducible without any infrastructure configurations. After modifying infrastructure configurations, we raise bitwise reproducibility by 18.6%, but 78.7% of buildable Dockerfiles remain non-reproducible. We analyze the root causes of the remaining differences, and find that beyond timestamps and metadata, developer-controlled choices such as uncleaned caches, logs, documentation, and floating versions are dominant causes of non-reproducibility. We derive concrete Dockerfile guidelines from these patterns and discuss how they can inform future linters and Continuous Integration (CI) checks for reproducible containers.