Chris Wanstrath suggests a standardized method for storing GitHub credentials to streamline integration with tools like GitNub and GitX, which often require frequent re-entry of usernames and API tokens. By configuring global settings in Git with the commands for username and token, users can facilitate easy access for applications and scripts, and directly modify the ~/.gitconfig file. Wanstrath has updated his gist script and gist.el mode to utilize this approach, providing examples in Ruby and Emacs Lisp, and encourages developers to adopt this method for improved user experience.