I'm using Firefox and have the "uBlock Origin" add-on installed. With it I can "right-click" an image and select "Block element…" to create a block for that specific image. I don't see a way to block them all.
EDIT: I do see a way now. If I open uBlock Origin preferences I can add "https://forums.macrumors.com/data/avatars/" to the filter list. This blocks the custom avatars.
It would be great if the ability to do that was brought back (in the sense of it being something that was available in the older forum software as I recall).
That appears to filter out pretty much all custom avatars. This does not affect any of this site's generic avatars (the ones with an alphabetical initial based on the first letter of the user's handle name) like 'S' for Saturn007 or 'C' for C DM.
It took me less than two minutes to figure this out. I scrolled through ten pages of one of the most popular threads in Community Discussion and I did not see any rogue avatar images. Thus the MacRumors operators are likely just using two sources for custom avatars: their own database (of individually uploaded images such as my own) and Gravatar.
Note that this method filters out all content below that URL string. In particular, you are universally wiping out ALL Gravatar avatars, not just at MacRumors but every site that you visit that uses this standard. It's sort of the Death Star approach but I am very often okay with that scorched earth methodology when dealing with Internet annoyances and/or security concerns.
You could block a specific avatar by putting in the entire URL for the image instead of the code that filters out everything from a website URL path.