Branch protection rule errors occur when pushing to protected branches like `main` or `master`, which may have rules requiring pull requests, code reviews, or successful status checks before allowing merges or direct pushes. To address this, verify the protection settings under *Settings > Branches* in GitHub, where you’ll see specific requirements. If the branch mandates code reviews, initiate a pull request and request reviewers to approve it before merging. If status checks are required, ensure all necessary tests pass in GitHub Actions or third-party CI/CD integrations. Alternatively, create a feature branch for new changes, which you can merge into the protected branch once all rules are satisfied. Branch protection ensures quality control, and by following the rules, you maintain the repository’s integrity.