Target \'AAA-Pods\' for project \'Pods\' was rejected as an implicit dependency for \'Pods_AAA.framework\' because its architectures \'x86_64\' didn\'t contain all required
On a very new project on Xcode 9.4.1, the issue was that my Podfile's deployment target was set to platform :ios, '11.0' while my project's iOS deployment target was set to 10.3.
This caused the generated Pods project to target iOS 11.0 (supported by only 64-bit devices on arm64 architecture), but since my main project targets 10.3 and includes armv7 devices, this doesn't work when archiving a Release build since a Release build also builds nonactive architectures by nature (unless you only support iOS 11 devices).
The fix then is to simply change the Podfile's deployment target to match your main project's, in my case it's platform :ios, '10.3'. Afterwards, run pod update and the Pods project should be regenerated. Launch Xcode, perform a clean and you should be able to run the archive process.