Say NO. Tell the bastards to get a warrant. If its important enough, Customs/ICE should able to convince a judge quickly they need a warrant to conduct a search of your private property. They are very clear on the law and procedure and simply want to bully, delay and cajole you into giving permission.
This advise was given to me not by some libertarian cranks, but by expensive DC lawyers who were former Federal Prosecutors and DOJ attorneys. They said - when you give permission, you allow law enforcement to go on a fishing expedition of anything and everything. DON'T DO IT.
The sensible thing to do though is not carry things in your wallet smartphone that you don't need to have in it. But it's so convenient to put everything in the phone...
In their country, their rules; maybe they don' need no stinkin' warrant!