In iOS 12 it is possible to allow unmanaged apps to access managed contacts.
Is this option available in Intune?
this is a relatively new option (iOS 12) and it's currently not available. But I'm quite sure MS will have a look at it. They look at every settings which are new in iOS and Android.
I solved it by creating a custom profile in the Apple Configurator tool and importing that profile in Intune.
Could you please provide additional context around this @Ronald Meer? The change made by iOS in OS 11.3+ was to start treating contacts as managed content based on this post: https://blogs.technet.microsoft.com/intunesupport/2018/04/17/support-tip-ios-11-3-and-native-contact...