BrowserStack uses a custom streaming method to stream video content in real-time from remote devices/browsers to your local browser to facilitate testing on BrowserStack.
Developer mode is enabled on our remote devices within our infrastructure to support the streaming method. Hence, Developer mode cannot be disabled on BrowserStack devices at the moment.
If your application requires Developer mode to be disabled, then the only workaround would be to disable this check for the application to proceed with testing on BrowserStack.