As I understand, they're acting as an agent of the government, it's a private company. So, the 4th amendment protecting against unreasonable searches _by the government_ does not apply.
if they WERE NOT acting as an agent then the 4th would not apply. I think they way they get around that is not do not report to the FBI but instead to NCMEC a "non-profit"
you do not want criminals to escape justice to do you???? /s
If a private citizen, on their own initiative, searches your house, finds contraband, and reports it to the government, they may be guilty of a variety of torts and crimes (both civil and criminal trespass, among others, are possibilities), there is no fourth amendment violation.
If a police officer asks them to do it, though, there is a different story.
No. The courts have already explicitly rejected the entity that NCMEC is a private entity. NCMEC can only handle child porn via special legislative permission and is 99% funded by the government.
The searches here are lawful because Apple searches out of their own free will and commercial interest and when there is something detected their employees search your private communications (which the EULA permits).
This is also why Apple must review the matches before reporting them-- if they just matched an NCMEC database and blindly forwarded then to NCMEC then it would be the NCMEC conducting the search and a warrant would be required.
It applies to private actors acting as agents of the government, it doesn't apply to private actors who for private reasons not directed by the government conduct searches and report suspicious results to the government (other property and privacy laws might, though.)
But the 4th Amendment would cover Apple being forced to modify their system to scan for anything else the Government has told them to.