Your Shopify theme does not contain private, sensitive information like keys and passwords since it is all available publicly to your shop visitors.
Because of this having your theme in a public GitHub repository does not pose a security risk.
Your shop is already publicly available to your competitors who could clone it if they wish using free tools to download all of your HTML, CSS and JS. A public GitHub repository makes this a bit easier, but it's likely your products / customers / marketing / service are what makes your business defensible and not your code.
If this is still a concern, Plug in Git works well with private GitHub repositories which are available on a paid GitHub plan.