And just last year, Mio Sugita, an L.D.P. lawmaker and protégée of Mr. Abe’s, said that same-sex couples “don’t produce children,” adding, “they lack productivity and, therefore, do not contribute to the prosperity of the nation. ”

The Abe government’s penchant for historical revisionism — for glorifying Japan’s wartime past, for denying that the Japanese military committed atrocities — is well documented. Several photos have emerged showing the L.D.P.’s policy chief and two members of Mr. Abe’s cabinet with neo-Nazis and far-right hate groups. In 2016, the minister in charge of Okinawa affairs refused to denounce a police officer’s pejorative and racist slurs (“natives,” “Chinamen”) against protesters opposing the presence of United States military bases in the prefecture. Again, Mr. Abe did not dismiss any of these ministers .

The Abe administration is, in other words, rejecting the rules of the democratic game, denying the legitimacy of its opponents, curtailing the civil liberties of dissenters and tolerating or encouraging some forms of hate speech — all precisely the indicators of budding authoritarianism that the political scientists Steven Levitsky and Daniel Ziblatt warn about in their 2018 book “How Democracies Die.”

While the book focuses on Mr. Trump, it also touches on other notable cases of elected leaders who have perverted the democratic process , including Hugo Chávez of Venezuela and Viktor Orban of Hungary. Yet it does not mention Mr. Abe, even though he, too, meets the authors’ criteria.

The oversight is common, and it is revealing.

As illiberal populism destabilizes the West, Japan’s allies and partners see Mr. Abe as a guardian of the international liberal order — despite his own illiberal record at home.

Michael Green, a former staffer on the National Security Council under George W. Bush now at the Center for Strategic and International Studies, has argued that “domestic political stability” in Japan has allowed Mr. Abe “to prioritize his foreign policy agenda” and work on “shaping regional and global institutions to preserve the rules-based international order.” According to the Lowy Institute, a leading think tank in Australia, “Japan has become the leader of the liberal order in Asia.” Prime Minister Scott Morrison of Australia has called Mr. Abe “the senior figure” in the region and said he “leaned on” Mr. Abe’s “real wisdom.”

How has Mr. Abe come to seem so benevolent?

The simplest answer may be that he is not a populist outsider, but an ultimate establishment insider: the grandson of Nobusuke Kishi, a prime minister (and suspected war criminal). Mr. Abe came to power without needing to ride any highly visible and disruptive movement; his rise didn’t call attention.