Alexis,
Imgur is a separate service from what Esri uses. Governments will always block sites like these. The only way around it is to have the map developer use a different site (like upload directly to ArcGIS Online) or have your network people allow certain sites (which likely won't happen).
Out of curiosity, which government are you with (state, local, fed, etc.)? Can you view pictures from sites like Flickr.com Google Photos and other photo hosting sites? This info would be good to know for people who make story maps and share them with governments.