“This is about morals,” said Steven Drahozal, the chair of the Dubuque County Democrats in Iowa. He said voters in Iowa, the critical early primary state, will actually appreciate a candidate who recognizes and acknowledges previous shortcomings. But he said Democratic candidates need to be acutely sensitive to those who in the past have been left behind. “Not intending to offend is not an excuse,’’ he said.

What is less clear is whether what works in a primary will be harmful in the general election and whether the cascade of apologies risks making Democrats look like the hypersensitive, politically correct crowd Republicans make them out to be — especially when compared with President Trump, who often insults and offends people and almost never apologizes for anything.

The zero tolerance on issues of race also played out in the almost immediate demands by nearly all the Democratic presidential candidates that Gov. Ralph Northam of Virginia resign over a racist yearbook photo. (Mr. Northam began with an apology but pivoted to a new defense when he triggered a crush of calls for him to resign.)

Political strategists and crisis communication experts said the sensitivity speaks to how quickly the center of gravity has shifted for Democrats on key issues. As recently as 2006, national Democrats including former President Barack Obama expressed wariness about immigrants’ ability to assimilate into American culture and did not openly embrace gay marriage — two talking points that would probably be deeply damaging for any 2020 candidate.

For candidates seeking to lead the party into its post-Obama era, their hope is that the base is more concerned with defeating President Trump and Republicans than holding every candidate to rigid standards of ideological purity.