In a series of columns for National Review in the early 2000s, Mr. Moore mocked female athletes and proposed, in what he says was a joke, that women be barred from officiating, announcing or even serving beer at N.C.A.A. men’s basketball tournament games. “Is there no area in life where men can take vacation from women?” he wrote in 2002. “What’s next? Women invited to bachelor parties? Women in combat? (Oh yeah, they’ve done that already.)”

Mr. Moore is a longtime economic commentator and writer, who has worked for conservative think tanks and the Wall Street Journal editorial board, and he founded the anti-tax Club for Growth. He did not respond to several requests for comment on Tuesday about his past writings, many of which are available in online archives and news databases.

In an appearance on Tuesday on a North Dakota radio show, Mr. Moore said his critics are “pulling a Kavanaugh against me,” in a reference to Justice Brett M. Kavanaugh, whose Supreme Court confirmation hearings were dominated by testimony from Christine Blasey Ford, who said Mr. Kavanaugh sexually assaulted her while they were both in high school. Mr. Kavanaugh disputed the claims and denied he ever assaulted her, rallying Republican senators to his defense.

Mr. Moore has retained a Virginia public relations firm that supported Mr. Kavanaugh during his hearings.

“I was so honored when I got the call from Donald Trump,” Mr. Moore said on the radio program. “But you know, all it’s been since then is one personal assault after another, a kind of character assassination that has nothing to do with economics. But you know, my divorce 10 years ago, or something I wrote 25 years ago. They have six full-time investigative reporters looking into me at The Washington Post, The New York Times, CNN. You know Scott, I kind of wear it as a badge of honor, that they’re so afraid of me.”

While many of Mr. Moore’s columns are written with sarcasm, they contain controversial statements that could raise questions about Mr. Moore’s actual views toward women. Mr. Moore has already been criticized by Democrats for his failure to pay more than $300,000 in child support to his former wife, Allison Moore, which resulted in Mr. Moore being held in contempt of court in 2013.

Mr. Moore has also been criticized as a loyalist for Mr. Trump who will largely be a proxy for the president at the Fed.