There is a solution to this, but it is a PITA.
You can encrypt your laptop using an essentially random password, something you can't possible remember, written on a piece of paper or in an email. Then leave the password in the care of a friend/spouse/coworker. Cross the border -- if they demand the password, you can honestly tell them you don't know it, that your friend has the password, and helpfully provide the phone number for your friend.
Then they can call your friend, and reach an individual who is NOT at the border, who has full jurisdictional protection, and your friend can honestly reply, "Sure I'll give you that password, just as soon as you show me a warrant."
With this approach you co-operate with the border guards to the best of your abilities giving fully honest answers as complete as you can make them -- it is simply beyond your power to give them the password, and they cannot compel the person who does have it.
Of course, once you clear the border to a location where you once again have rights, your friend happily provides you the password and you unlock your laptop and carry on.