WASHINGTON — After all of the entreaties from top Republicans to show respect at Judge Ketanji Brown Jackson’s confirmation hearings, Senator Ted Cruz on Tuesday afternoon chose to grill the first Black woman nominated for the Supreme Court on her views on critical race theory and insinuate that she was soft on child sexual abuse.

The message from the Texas Republican seemed clear: A Black woman vying for a lifetime appointment on the highest court in the land would, Mr. Cruz suggested, coddle criminals, go easy on pedophiles and subject white people to the view that they were, by nature, oppressors.

The attack, the most dramatic of several launched from inside and outside the Senate Judiciary Committee’s hearing room, contained barely coded appeals to racism and clear nods to the fringes of the conservative world. Two other Republican senators, Josh Hawley of Missouri and Marsha Blackburn of Tennessee, had already signaled they would go after Judge Jackson by accusing her of having a soft spot for criminals, especially pedophiles, and an allegiance to “woke” racialized education. Senator Tom Cotton, Republican of Arkansas, also pressed the issue on Tuesday night.

None of those issues were connected to cases coming before the Supreme Court — or to cases ever decided by the court. They were amplified outside the chamber by institutional Republicans and the conservative media. Fox News ran a headline reading “Ketanji Brown Jackson serves on board of school that promotes critical race theory,” and the Republican National Committee shared a GIF on Twitter showing the judge’s picture with her initials, “KBJ,” crossed out and replaced by “CRT.”

“I do think it’s a legitimate question to ask — would they be asking these questions if this were not a Black woman?” bristled Senator Raphael Warnock, Democrat of Georgia, who is also Black.

The list of skeptical questions about Judge Jackson’s record read like a compendium of political touchstones animating Republican politicians and voters: critical race theory, parental rights, mask mandates and transgender women in sports.

Mr. Cruz went after The New York Times’s “1619 Project,” a favorite target of the right, and held up a pile of books that he said had been plucked from the library of the expensive private school in Washington on whose board Judge Jackson sits. All of them, he argued, espoused critical race theory, a graduate school framework that has become a loose shorthand for a contentious debate on how to address race. Mr. Cruz slammed critical race theory as “framing all of society as a fundamental and intractable battle between the races.”

But central to the Republican message was the “soft on crime” aspersion, a line of attack that raised the specter of criminal defendants — many of them Black — coddled by a liberal justice system that they suggested Judge Jackson embodied.

Along similar lines, Republicans contended that the nominee had been especially lenient on purveyors of child sexual abuse imagery, a claim that spoke to a fixation of those wedded to the QAnon conspiracy theory. Many of its followers — some of whom took note online of the Republican line of questioning at the hearings — falsely believe that former President Donald J. Trump is fighting a cabal of elites including top Democrats who are in fact child traffickers and pedophiles.

“I believe you care for children, obviously your children and other children,” Mr. Cruz told the nominee. “But I also see a record of activism and advocacy as it concerns sexual predators that stems back decades, and that is concerning.”

The characterizations were a far cry from the reputation of a federal judge who has garnered wide respect in legal circles and has already navigated three previous — and far more mild — confirmation processes. Over her nine years as a federal judge, first on the United States District Court for the District of Columbia and later on the U.S. Court of Appeals for the D.C. Circuit, her supporters say, Judge Jackson has molded herself after the retiring justice she is to replace, Stephen G. Breyer, for whom she clerked and who was known as a consensus builder.

Her younger brother patrolled the streets of Baltimore as a police officer, and two of her uncles were career law enforcement officers. “As someone who has had family members on patrol and in the line of fire, I care deeply about public safety,” Judge Jackson said.

Allegations of being soft on crime have been a standard line of attack from Republicans against Democrats’ judicial nominees and candidates since at least the Nixon era, political scientists said. They are part of a strain of criticism that Black public servants in particular have come to expect, said Justin Hansford, a Howard University law professor and the executive director of the Thurgood Marshall Civil Rights Center. “It is a dog whistle, and it plays to a certain audience,” he said.

Thurgood Marshall, the nation’s first Black Supreme Court justice, faced similarly coded language during his confirmation hearing 55 years ago, when a group of fervently segregationist senators tried to stir fear over clashes between civil rights protesters and the police, as well as crime on American streets.

But to Mark Victor Tushnet, a Harvard law professor who clerked for Justice Marshall, the attacks against Judge Jackson have been far less veiled than those against Justice Marshall.

“Dog whistles are supposed to be things that you can’t hear but that you receive in the subconscious,” Mr. Tushnet said. “This is all quite open.”

Few claims could be as incendiary as the assertion that Judge Jackson had been lenient on the sentencing of people found guilty of consuming or distributing child sexual abuse imagery.

Even an opponent of the judge’s confirmation, writing in the conservative National Review, dismissed the accusation as “meritless to the point of demagoguery.”

But conservative senators were determined. On Tuesday evening, Mr. Hawley dug into one case that came before Judge Jackson involving an 18-year-old. The senator tallied the sex acts, violence and abuse portrayed in dozens of videos and images found on the man’s computer. The prosecutor asked for a two-year sentence; Judge Jackson gave him three months.

“He’s got images the government said added up to over 600 images, gobs of video footage of these children, but you say this does not signal a heinous or egregious child pornography offense?” Mr. Hawley asked incredulously. “Help me understand that — what word would you use?”

Judge Jackson responded with some exasperation as she listed the factors a judge must consider in such cases, including the guidelines, a defendant’s age and the harm to the victims. “Sentencing is a discretionary act of a judge, but it’s not a numbers game,” she said.

By making the leniency allegations, Mr. Cruz, Ms. Blackburn and Mr. Hawley appeared to be exploiting echoes of QAnon, which has a broad, almost cultlike reach among some members of the Republican base. The theory was a kind of mutation of an earlier online fiction, known as PizzaGate, which held that Hillary Clinton and her allies were involved in a child sex trafficking ring headquartered in the basement of a Washington pizzeria. (In 2017, Judge Jackson sentenced a man to four years in prison after he fired a rifle inside the pizzeria.)

One prominent QAnon message board immediately amplified the Republican allegations with a post on Tuesday afternoon that wildly and baselessly claimed that there was proof in Judge Jackson’s “office logs” that she sympathized with child abusers. On Monday, after Mr. Hawley’s remarks on the hearing’s first day, the same website posted a message with copies of the senator’s tweets about Judge Jackson and the subject heading, “Biden’s SCOTUS nominee has got a soft spot for pedophiles.”

Judge Jackson forcefully pushed back against the claims. In remarks responding to Mr. Hawley’s questioning, she flashed a rare sign of emotion, alluding to her own motherhood and her disgust with child sexual abuse imagery.

“These are some of the most difficult cases that a judge has to deal with because we are talking about pictures of sex abuse of children,” she said. “We are talking about graphic descriptions that judges have to read and consider.”

Republicans have also spoken angrily about liberal intrusions on public education, but a key attack against Judge Jackson on Tuesday centered on her seat on the board of a left-leaning private school in Washington, Georgetown Day School, where kindergarten tuition is $39,896 a year.

Ms. Blackburn painted the parents of Georgetown Day students as unwitting dupes, subjected to “white privilege” education and anti-racist programming.

Judge Jackson traced the school’s founding to the segregated Washington of 1945.

“Three white families, Jewish families, got together with three Black families and said that despite the fact that the law requires us to separate, despite the fact that the law is set up to make sure that Black children are not treated the same as everyone else, we are going to form a private school so that our children can go to school together,” she said.

Mr. Cruz was unmoved: “OK, so you agree critical race theory is taught at Georgetown Day School.”

Alan Feuer contributed reporting.