How can I use one Github branch for multiple identical Shopify stores?

We’ve just begun using it. So far it works flawlessly.

It will require some hands on action when installing a new app, to avoid conflicts (if app injects code, it will come from the theme to github affecting non-setting files, and you’re heading towards a conflict). But for code changes coming from your editor, and avoiding changing or conflicting with the settings pushed to github from the live theme, it works smooth.