If I have the Smush Pro CDN active no images are loaded on my site. If I disable it, the images are properly displayed.
I tried running a plugin/theme conflict test and the issue is still there.
I contacted my host to check if the server's firewall could be blocking smushcdn.com and they told me:
"Can you ask them what user-agent they're connecting from, please? I cannot see any non-200s in the logs for anything resembling a Smush connection, so doesn't look like a block our side, though I can confirm that better with a user-agent."