if user A circulates cat pictures, user B circulates dog pictures, and user C circulates both, can user A block dog pictures from B and C, but still see user C’s cat pictures?

To do that, you need either a system of trust where you trust someone else to tell you which images from C are dogs and which ones are cats (as well as a policy for what to do when a picture contains both), or an automated system that will scan all the messages and perform that determination for you.