I'm not sure if there is such an app already, but if there isn't (I couldn't find one), I'm just putting the idea out there.
An app that automatically exports any Shopify blog posts to FB (Twitter, G+...) would be a great time saver.
Posterous used to do this. It would auto post to Shopify, Twitter, Tumblr etc. You may want to see if that is still an option.
You can auto-post to Facebook from Shopify blogs with OneUp: https://blog.oneupapp.io/autopost-shopify-products-to-facebook/
You can use zapier to create a workflow. Just use the trigger of new blog entry: https://zapier.com/apps/shopify/integrations