Leading law scholars are warning that the US supreme court faces months or even years of bitter dispute over whether its new recruit, Brett Kavanaugh, should recuse himself from cases involving sexual violence and party-political partisanship.

Kavanaugh finally took his seat on the country’s highest court on Tuesday with sexual assault allegations unresolved and his highly contentious testimony before the US Senate still reverberating. During his historically ugly confirmation process, he was accused by three women of sexual misconduct.

None of the allegations were proven. But nor were they – as Donald Trump falsely claimed during the swearing in ceremony on Monday – disproven.

How the initial allegations will play out is now a matter of urgent legal debate, as are the accusations of partisanship he leveled at Democratic senators when he claimed they had orchestrated a leftwing conspiracy against him. The most direct questions raised are likely to relate to cases coming before the new court on sexual violence or discrimination.

Already percolating their way up the judicial chain and heading for the supreme court are suits demanding that gay and lesbian people be entitled to the same constitutional protections against workplace discrimination as are afforded employees on the basis of sex, race, color, national origin and religion.

Other cases that might come before the 53-year-old Kavanaugh – who holds his seat on the court for life – include cases on sexual assault on campuses, family law cases and suits involving the right of those accused of domestic violence to buy guns.

Julie Goldscheld, professor of law specializing in gender issues at CUNY School of Law in New York, said that she was concerned about Kavanaugh’s ability to sit impartially in judgment over such matters. “His testimony compounded my concerns both about his temperament and potential bias around issues relating to gender violence, employment discrimination, or any contexts in which sexual assault comes up,” she said.

Goldscheld was one of 2,600 law professors – about a quarter of all full-time law scholars in the country – who signed a joint letter opposing Kavanaugh’s confirmation. One of its organizers, Bernard Harcourt, professor of law and political science at Columbia University, told the Guardian that another major area of concern relates to cases with a party-political bearing, given Kavanaugh’s highly partisan performance in front of the Senate judiciary committee.

In a fraught hearing of the committee following testimony from his main accuser, Dr Christine Blasey Ford, Kavanaugh aggressively defended himself in party-political terms. He accused Democratic senators on the panel of waging a “calculated and orchestrated political hit” against him, “fueled with apparent pent-up anger about President Trump and the 2016 election … revenge on behalf of the Clintons and millions of dollars in money from outside leftwing opposition groups”.

Protesters gather outside of the supreme court against Justice Brett Kavanaugh on his first day at the supreme court in Washington on Tuesday. Photograph: UPI/Barcroft Images

Later, he admitted in the Wall Street Journal that he had “said a few things I should not have said”, without specifying the actual comments.

Supreme court justices in the past have displayed partisan behavior, such as the late Antonin Scalia and Clarence Thomas who provoked criticism when they attended a 2010 strategy summit hosted by the far-rightwing Koch brothers. But never before have justices revealed their own party-political allegiances so viscerally in public.

Harcourt said that the “hidden face of Brett Kavanaugh was exposed. We saw his true bitter partisanship.”

Such a display would have ramifications for any case coming before the court that had clear partisan lines, Harcourt said. “Anything that affects partisan politics is now tainted – as is most apparent with voting rights issues such as redistricting and cases on gerrymandering.”

The supreme court has often been asked to adjudicate over changes to electoral law in which Republican-controlled states have been accused of seeking an unfair advantage by redrawing constituency lines or suppressing the turnout of Democratic-leaning minority voters. The most recent was a case involving Ohio’s purge of thousands of voters from its rolls.

In the outcome, the supreme court voted 5 to 4 in favor of Ohio Republicans, with Anthony Kennedy wielding his swing vote. Now that Kennedy has been replaced with Kavanaugh, a justice with glaring partisan tendencies, such a narrow majority ruling could be considered improper by large numbers of Americans.

The most partisan issue of all would be impeachment. If the Democrats took back the House of Representatives in the midterm elections next month, they would be in a position to press charges against Trump in the wake of the Robert Mueller investigation on Russian interference in the 2016 election.

“Any kind of issue closely related to impeachment or investigations of possible corruption or tax fraud – any of those issues would fall squarely in the bailiwick of deeply partisan politics,” Harcourt said. “That would in turn trigger doubts about Kavanaugh’s conspiratorial thinking that was evident during his confirmation.”

In all such cases, a central dispute is likely to be whether Kavanaugh should recuse himself. The US supreme court is unique among federal courts in that the justices effectively police themselves – a practice that has been widely criticized.

The nine justices can and do recuse themselves, frequently without explanation. Litigants, if they dare, can also file a motion calling on individual justices to step aside for reasons of conflict, but the decision is left to the justice in question with no right to challenge the outcome.

The pattern has been seen with Clarence Thomas who was accused during his 1991 confirmation process of sexually harassing Anita Hill. Thomas has gone on to sit on several cases relating to sexual harassment in the workplace, without recusing himself.

Judith Resnik, Arthur Liman professor of law at Yale Law School, said Kavanaugh’s presence, given what happened during the confirmation, had “put a pall over the supreme court. The Senate hearings were shocking, and have left a terrible aftertaste.”

She added: “Kavanaugh has so aligned himself with the Republican party it casts a shadow: will he be able to judge cases which would expressly benefit the Republicans?”