Why does my Mac keeping connecting to Apple?
It could be the softwareupdated process which is looking to see if there are any available OSX / macOS patches or updates to other App Store applications.

You might see an improvement if you disable automatic software updates. This should be possible by going to System Preferences -> App Store and then unchecking the option for "Automatically Check for Updates".

Of course, this means that you won't get automatic updates anymore and you'll have to check manually from time-to-time.