The US government is charging Julian Assange with conspiring to hack into a government computer. They’re not charging him with publishing secret government documents, which would violate his First Amendment rights and threaten news outlets everywhere. The New York Times wasn’t tried for publishing the Pentagon Papers, which had been stolen from the government by Daniel Ellsberg.
The question is, will Assange ever be extradited to the US? If Assange chooses to fight extradition (and why wouldn’t he?), the process could take years to resolve itself. Jeremy Corbin, who wants to be prime minister of the UK, is against extraditing Assange. I don’t know PM May’s view, but she might not be PM much longer the way things are going with the Brexit fiasco.