Hi everyone
I too have been suffering with the issue of call syncing but - finally - I've FINALLY managed to figure out the cause.
I have 2 iPhones, one for work and one personal. Like most people I have signed into the same Apple ID on both of these (for both Store and iCloud) so that I can share my purchased media between them, and also ensure that I backup both devices. This is not the cause of the issue, however - and neither is FaceTime, iMessage, Call Forwarding, Handoff or any other other issues mentioned this thread. The issue is iCloud Drive.
At some point in recent history, Apple must have begun backing up our call lists within iCloud Drive, as switching it on on both devices is enough to immediately start the lists syncing again. I have made the decision to switch off iCloud Drive permanently on my work phone to avoid the issue. Naturally, you only have to switch it off on ONE device to prevent the sync.
Is it annoying? Yes, a little. There aren't many apps on my work iPhone but it would have been nice to have the option to share/backup data with iCloud Drive where available. Perhaps Apple shouldn't have implemented this feature for call lists OR should have made it merely an option.
However - to the people that have used this thread to continuously repeat their opinion that you shouldn't share Apple IDs - I don't share Apple IDs with anyone else and I still had the problem due to my unique circumstances. You said that sharing Apple IDs was the only cause, this wasn't entirely correct as we can now see. I personally do agree that you shouldn't share Apple IDs, however please let us all learn from this, that sometimes there may genuinely be other reasons for problems occurring, as was the case here. I agree with your viewpoint BUT you couldn't see past your own opinion to think about what ELSE may be causing it, which is a shame as it has caused so much ill feeling in this thread. We're all Apple fans, let's play nice :-)
I hope this helps other people that have had the issue! AND - if you are sharing Apple IDs - why not at least consider having separate IDs for iCloud? You can still share an ID for Store purchases (you shouldn't, but who am I to try stopping you :-) ), but at least this way you'll avoid the issues raised in this topic.