I just checked my submission, which got denied. Here is the response (which seems to just be a generic response):
General issues:
Invalid Use Case: The use case described in your submission notes, screencast and website is not a valid use case that we allow on our Platform. Please see our Permissions Review and valid use cases description (https://www.instagram.com/developer/review/) for more information.
public_content:
This permission (public_content) does not support the use case you described in your submission notes, screencast and website. Please review Login Permissions (http://instagram.com/developer/authorization/) for a comprehensive list of permissions and valid use cases.
I’m honestly not sure what they are looking for, or what I could possibly change to “meet their requirements” which are pretty vague. The requirements can be found here https://www.instagram.com/developer/review/
As of right now I think I may just have to scrap my plugin and be done with Instagram. If someone actually gets an app approved please let us know what your app is and how you did it…