Blix has previously accused Apple of unfairly suppressing Blue Mail. It claimed that Apple's acknowledged problems with App Store rankings pushed Blue Mail down to 143rd in search results (it's since back to 13th). It also disputed Apple's statement that it removed Blue Mail from the Mac App Store for supposedly copying another program, TypeApp. The developer said that TypeApp had been voluntarily removed and that Apple was promoting market monopolization by limiting the number of competing apps.
It's too soon to know who will prevail. If Blix succeeds, though, Apple faces both an injunction as well as damage claims. It wouldn't necessarily have to modify Sign in with Apple, but it might have to compensate Blix to keep using the privacy-minded concept.