Unless I missed a big part of this story Apple isn't being compelled by a court to comply - so if the presence of this tech causes a larger PR stink than publicly backing out of the rollout then Apple will read the writing on the wall.
Public and political pressure is definitely an issue - but it's still soft-pressure so applying more pressure in the other direction will be compelling to Apple.
Just to clarify, this "on device content control" defies all the benefits of the E2E encryption because it is "at the end". It will enable Apple to implement E2E and give the authorities a channel to program the devices to report users in possession of content deemed unacceptable by the authorities.
Public and political pressure is definitely an issue - but it's still soft-pressure so applying more pressure in the other direction will be compelling to Apple.