Can't sync or even access contacts of Moto G4 / E4 and fresh Android 7.1.1

**tl;dr** I can't access or sync my contacts on two phones with freshly installed Android 7.1.1 while I can access and sync them without problems on third phone, with Android 6.0, connected to the same Gmail account. ---- Whenever I try to access contacts on my Moto E4 or Moto G4 with Android 7.1.1 I see following: This process is endless. It last 12+ hours so far. I have no problems accessing my contacts on my Moto E3 (Android 6.0.1), which is connected to the same Gmail account as my Moto G4 is. It seems that contacts are inaccessible due account not being able to sync them: As you can see (left screeenshot - Moto G4 / Moto E4), the _Peoples details_ item cannot be sync for past two days (since getting this phone) and I don't even have _Contacts_ sync item on the list. Everything is OK on Moto E3 (right screenshot). Steps taken so far: - phone restart, - removing Google account and adding it back again, - checking on different network access type (i.e. LTE instead of WiFi). No luck so far. What else can I check or do?