When disabling unity audio completely through Edit->Project Settings->Audio->Disable Unity Audio and using FMOD instead the option "Mute Other Audio Sources" (Edit->Project Settings->Player->Other Settings->Mute Other Audio Sources) is ignored. It will always mute other audio sources, no matter if enabled or not.

Steps:
1. Download project from Google Drive (MuteAudioSourcesBug.zip)
2. On iOS device play music (recommended: Podcasts)
3. Build and Run on iOS device

Expected behavior: external music continues to play.
Actual behavior: external music stops.

Reproduced with: 2018.1.0a1, 5.6.4p1.

Note: not reproducible on Android.

Tested with: iPhone 6S iOS11.0; Motorola Nexus 6 Android 6.0.

BY DESIGN:
The "Mute Other Audio Sources" option only affects the built-in Unity audio settings.

Once users wish to use the FMOD Studio integration they will need to (a) disable Unity audio from the Edit > Project Settings > Audio menu, and (b) manually set the iOS Audio Sessions to allow for background and/or interrupting audio. This is mentioned in the iOS Specific Starter Guide of the iOS API.

If you want the audio from Unity (FMOD) to mix with other system audio, you can override this behavior by setting the AVAudioSessionCategoryOptionMixWithOthers option on the session.

This is not a bug but intended behaviour.