Do you see any message when you upload avatar? Have you tried to change it when on only one certain wiki? What device and browser are you using?
If you've only tried to change it on one wiki (e.g. here on Community Central), then try changing on some other wiki instead. Also, there can be issues with changing avatar on mobile so if you're trying on mobile, try on computer instead.
Edit: My bad, I wasn't informed quite right. Thank you for informing, Andrewds.
The reason why it doesn't work on some wikis is because local permissions impact the avatar upload process even though the avatar is a global thing. Here on Community Central, this should not be an issue. If you tried on Community Central and it did not work, then it is likely a different issue.
Uploading from mobile devices is fine. The issue it typically the image users are trying to upload. There is a size limit on avatars and most (if not all) images produced by mobile devices (whether by camera or screenshot) are much larger than this limit. As long as the image meets the restrictions for avatars, it shouldn't matter whether or not you are uploading from a mobile device.