The thumbnail of an image configured through the Pop-up Media box in ArcGIS Online does not display in a feature pop-up in ArcGIS Online if the image URL contains the number sign (#).
The image link with with # is actually a HTML page - not an image. A HTML element will not be able to display a HTML page.
Ideally, when copying images from Wikipedia, we should right click the image and select Copy Image Location to copy the actual URL. For this case the correct URK would be: https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Quake_epicenters_1963-98.png/300px-Quake_epicenters_1963-98.png