Comment by einpoklum

You mostly don't sync any such data. Prepare some file (or a few files, including an .ics for itinerary or what-not) with information about your trip, a few days in advance, and copy the file(s) to the phone. That's it.

And if you use iCloud or any of that stuff - you've already lost; Apple, and the US government already have access to your files and communications before you ever came to the airport. Sure, maybe it's not the specific border guards who have the access, but still.