We recently added WooCommerce capabilities to our site and hadn't noticed any issues before, but it appears that the FAQ Manager plugin messes with post types in a strange manner.
With FAQ Manager installed, wordpress shows all of the WooCommerce shop orders in the RSS feed. As soon as I disable FAQ Manager, the shop orders are hidden from the RSS feed... as they should be.
The WooCommerce default correctly hides the shop_order post type.
After disabling and enabling all plugins one by one, I was able to track down the problem to this plugin. FAQs are important for this website, so we've had to disable the RSS feed until this can be fixed. Please let me know what other information I can share to make fixing this easier. Thanks!