I have the same issue on two different phones, one with Android 5 and the latest Opera mini 33.0.2254, another one with Android 6 and 29.0.2254.

My guess, one of the Google updates is causing this issue, because I have the third phone with Android 4.4.2 and Opera mini 33.0.2254, where I rolled back Google Play Services to one of the oldest version (from 12.5.29 to 12.2.21), because Contacts app started crashing. Mini's private tabs work just fine on that phone.