The case upon which the whole border search exemption rests is United States vs. Ramsey, which strings together a whole bunch of prior decisions in an attempt to demonstrate that border searches are presumptively reasonable. One of the oldest references it reaches to is Boyd vs. United States. Turns out that Boyd justifies its holding based on the following notion:

The search for and seizure of stolen or forfeited goods, or goods liable to duties and concealed to avoid the payment thereof, are totally different things from a search for and seizure of a man's private books and papers for the purpose of obtaining information therein contained, or of using them as evidence against him. The two things differ toto coelo.

In the information age, these things don't differ "toto coelo" anymore and you cannot have different standards that apply to them. They are the same.

A border search of the contents of a laptop is precisely a search of a "man's private books and papers for the purpose of obtaining informaiton therein contained, or of using them as evidence against him." It is precisely the sort of search the Fourth Amendment was set against.

If the rights protected by the Fourth Amendment are to survive in this context the state must conceed.

BOYD V. UNITED STATES, 116 U. S. 616 (1886) -- US Supreme Court Cases from Justia & Oyez