For the past four years, Chinese businessman Guo Wengui has lived in an 18th-floor apartment at the Sherry-Netherland Hotel in New York, where he fires off social-media missives that purport to expose corruption at the highest levels of the Chinese government.

He said his efforts have rattled Beijing and that he has applied for U.S. asylum to protect himself. China hard-liners in the U.S., including President Trump’s former adviser Steve Bannon, have rallied to his side.

But...