I think you are talking about the GIF avatars
Yes, there is a way to block them by blocking all avatars, if you enable it, then you won't see any avatar, either GIF or the normal ones
For that you have to go to your Control Panel, then click "Edit Options". Then scroll down and under "Thread Display Options" you will see the options to see avatars, signatures and images. Disable the tick beside "Show Avatars" and then scroll down to the bottom of the page and click "Save Changes"
After this, you won't see any avatar in the threads. To view what avatar anybody has, you have to visit their Profile, where you can see their avatars, signatures, etc. I have the signatures disabled for a long time, so when I need to know what signature anybody has, I just visit their profile
But if you are talking about the GIFs in the posts, then you have to disable "Show Images" over there, but then you will not be able to see any type of image in the post
Hope this helps