There have been glowing personal tributes from women, scenes of friendly banter between Mr. Trump and immigrants and a Black family, and stories from people he reached out to in times of despair. If all political conventions cast their candidates in the best possible light, the Republican National Convention has been going all-out for bright and sunny…

Sarah Longwell, a longtime Republican strategist who opposes Mr. Trump, said the decision to show a version of him that most Americans don’t see was right, insofar as voters were looking for something to point to in order to justify their support for a president who has encouraged racist conspiracy theories, lashed out at women and repeatedly insulted the intelligence of his Black critics.

“If there are people who are looking for permission to vote for him,” Ms. Longwell said, “it does give them something to point to.”