Everyone proposing clever technical solutions. Burner phones and encrypted cloud data etc... you are solving the wrong problem. Instead of engineering a way for the few people who care deeply to avoid this at great effort, engineer a way for this to not be legal. Write your congressperson, donate time and money to political parties, make privacy at the border for ALL (not just citizens) a priority in every election.
the technical aspect of this issue is a solvable problem. the social and political aspects of it are not. there's no political traction against this stuff. the border patrol types are too stupid to understand simple and innocent explanations, and treating them as equals is a surefire way to incur their wrath. the way to make privacy at the border work for everyone is for everyone to conspire to keep the border patrol…
No, they're at least somewhat solveable. It's true that in the long term, those with power will use it to seek more power. But that would seem to imply that the government cannot be peacefully replaced every few years through voting, or that checks and balances cannot keep authoritarianism in check, and that's at least worked for a while. We just need to re-strengthen those limits and develop new rules to account for the new technology.
Temporary cultural issues and a lack of understanding are surmountable problems. But you're correct that this social and political change is a lot more difficult than encryption software.