Democratic senators didn’t have many questions for Justice Don Willett about his decisions and dissents as a member of the Texas Supreme Court. But at his Wednesday confirmation hearing for a seat on the Fifth U.S. Circuit Court of Appeals, they expressed grave concerns about his sense of humor.

Justice Willett is almost certainly the most conspicuous jurist on Twitter —or he was, until President Trump nominated him in September—and there were sure to be questions about his tweets. At some points, though, the senators seemed like science-fiction androids struggling to grasp the human concept of humor.

“You’ve equated the constitutional right to same-sex marriage, which the [U.S.] Supreme Court has upheld, with the constitutional right to marry bacon,” said Sen. Patrick Leahy of Vermont, the panel’s ranking Democrat. “I don’t think one would see that as praising the Supreme Court decisions.”

The April 2015 tweet in question read: “I could support recognizing a constitutional right to marry bacon.” It was accompanied by a stock photo of strips being fried. Mr. Leahy perceived a sizzling disdain for judicial precedent—never mind that the high court hadn’t made its decision at the time. It had heard oral arguments in Obergefell v. Hodges the day before Justice Willett tweeted.

Justice Willett, who regularly mentions that he doesn’t take political stances on Twitter, clarified that his tweet was an “attempt to inject a bit of levity” at a time when “the country was filled with rancor and polarization.”

To which Mr. Leahy replied: “And you think that cut back the divisiveness with a comment like that?”

Sen. Al Franken of Minnesota asked Mr. Willett about a tweet from February 2014: “Go away, A-Rod. ‘@FoxNews: California’s transgender law allows male high schooler to make girls’ softball team . . .’ ” The reference was to Alex Rodriguez, recently dropped from the New York Yankees.

Mr. Franken wanted to know if “it demonstrates good judgment for a man in his late 40s—a sitting Supreme Court justice—to publicly demean and humiliate a 17-year-old girl on Twitter.”

Justice Willett answered: “I believe that every child is a gift. Every child is a blessing.” While conceding that “it was a ham-handed attempt at levity,” he clarified that it “was an A-Rod tweet, not a transgender tweet.”

Mr. Franken, who has dabbled in comedy himself, said: “I don’t get it. But sometimes when you don’t get a joke, it’s because it wasn’t a joke.”

He ought to know. In 2008, during Mr. Franken’s first run for the Senate, he came under fire for having pitched a “Saturday Night Live” gag about using a date-rape drug on a prominent female journalist. That was in the mid-1990s, when Mr. Franken was in his 40s. On Thursday, model Leeann Tweeden accused Mr. Franken of forcibly kissing her while rehearsing a USO show in 2006, when the future senator was 55.

As for Mr. Leahy, hours after he browbeat Mr. Willett for his tweets, he retweeted a meme that mocked President Trump’s weight, contrasting it with President Obama’s fit figure. “I KNOW I shouldn’t have retweeted this,” the senator observed. “A moment of weakness . . .”

Only Sen. John Kennedy of Louisiana showed any interest in how Justice Willett would conduct himself as a federal judge. Whereas Mr. Kennedy asked about his views on fundamental rights, the Democrats were content to grill him about bacon.

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