I was thinking of changing mine for a while and you made me go through the process.
It didn't work from the ACF app so I tried from mobile site. In my case the problem was that I had the max number of different avatars allowed, so I had to delete a few of the old ones first. In the mobile site tap the cog icon above the search symbol, select Edit avatar or Profile and go from them.
I selected a previously cropped image of 640x640. In your gallery make it squared beforehand.