HONOLULU — President Obama celebrated a low-key Christmas in Hawaii this year. He sang carols, opened presents with his family, and visited a nearby military base to wish the troops “Mele Kalikimaka” — the Hawaiian phrase meaning “Merry Christmas.”

But the one thing the president and his family did not do — something they have rarely done since he entered the White House — was attend Christmas church services.

“He has not gone to church hardly at all, as president,” said Gary Scott Smith, the author of “Faith and the Presidency: From George Washington to George W. Bush,” adding that it is “very unusual for a president not to attend” Christmas services.

Historically, watching the nation’s first family head to church dressed in their Sunday best, especially around the holiday season, was something of a ritual. Yet Mr. Obama’s faith is a more complicated, more private, and perhaps — religious and presidential historians say — a more inclusive affair.