So today I have just enabled the SocialProfile extension on the Alternate History Wiki and as a test I tried to upload a picture to use as an avatar. It allowed me to choose an image from my local computer and the filename appearing next to that button. But after clicking "Upload file", it doesn't show the image in the page that shows the different sizes and when I leave the page where the avatar should be shows a missing image both on the profile banner with the Cosmos skin and on the userpage.
Checking to see if there were other conflicting or dependent extensions, I found out that avatars don't work for private wikis using image_auth.php
This issue seems to describe the same problem:
This gives me a clue because the wiki in question was set to private by the original founder but became public again when I adopted it. It seems it still has that permission error.
I uploaded my image on another site with SocialProfiles enabled and it successfully updated the avatar showing the image that I uploaded.