WASHINGTON — The Senate narrowly confirmed Jonathan Kobes as a federal appeals court judge on Tuesday even as the American Bar Association questioned his understanding of “complex legal analysis” and “knowledge of the law.”

Mr. Kobes, a 44-year-old aide to Senator Mike Rounds, Republican of South Dakota, is the second of President Trump’s judicial nominees to be confirmed whom the bar association deemed unqualified.

A number of other Trump nominees have raised concerns, including five who also received the unqualified rating. Others were rated as qualified but carried with them politically or racially insensitive remarks from their past that resurfaced during their confirmations. One wrote in an online forum that the nation’s commitment to diversity was tantamount to accepting “lower standards.”

To the chagrin of even some Republicans, their confirmation hearings have thrust politically sensitive topics into the spotlight at a time when the party is wrestling with issues of race and governing competence. Despite the controversies, they have all won the backing of most Republican senators, revealing how far they are willing to push the boundaries on their drive to reshape the judiciary as a conservative bastion.