The 4th amendment protects against unreasonable search and seizure, and the state must show cause for conducting any search. At a border crossing, search for contraband (including contraband plants and animals which can seriously damage the United States) are an exception because it's reasonable to search people at a border crossing.

https://en.wikipedia.org/wiki/Border_search_exception

Here, the EFF has to show that the search that was conducted wasn't reasonable in some manner or that it otherwise violates due process. They will need to show that the execution of the search wasn't reasonable, because being subject to a search in and of itself generally is. The only SCotUS ruling on search of electronic devices has been Riley v California (https://en.wikipedia.org/wiki/Riley_v._California) where they ruled that a search warrant was required to search an electronic device even when an individual has already been placed under arrest.

The government argues that searches at international borders is a "reasonable" search, thus the 4th amendment's prohibition on "unreasonable searches and seizures" doesn't apply.

The EFF disagrees. You can read their reasoning in the linked article.

It's clearly unreasonable: a customs search with the reasonable purpose of preventing contraband is used for massive intrusion in the personal life of specially selected people.

It's a way government can eschew all constitutional protection for private data, by simply waiting for the target to cross a border, practical for a majority of citizens. Data is substantially different from physical possessions because it's very portable and most people do indeed carry vast amounts with them when traveling.

Furthermore, in the modern world data import or export offenses (espionage) do not employ physical border crossings, so there is almost no reasonable offense the search could uncover.

Whose to also say that we can trust the people doing the searches? What if someone who has top secret government documents on their phone and it gets compromised? The person sells said documents to another state, or worse yet, one of them (or their systems) is compromised by foreign hackers? Now it's a data mining point and who would suspect them to be the root cause? I don't know enough about their systems or their hiring requirements to trust them with my phone. I much rather buy a travel phone that I can pop in a SIM card when I reach my destination and isolate the information available on it.

The word "reasonable" in this case is almost a term of art, meaning "the courts get to decide". Decide they have.

Note that the EFF is only disputing searches of electronic devices. Nobody contests that physical border searches are reasonable.

That makes sense now -- you're not going to be bringing in contraband plants or animals or drugs on your phone.

If people are being physically abused then it is completely unreasonable.