Detecting child abuse pictures is not incompatible with end-to-end encryption if the detection is done locally.

Facebook (or other messenger app owners) could train a good classification model to detect child abuse pictures on large servers and provide the model to smartphones locally. Before sending pictures, the app would run the trained model (which is cheap computationally). If if detects pictures of abuse with a certain accuracy, the app would block the transmission of the picture (possibly, explaining why to the user). If the detection of pictures of abuse happens again, the user could be banned from the app for 1 day, and if it happens more often the ban would become longer and longer.

That way facebook can fight child abuse without ever having the pictures.