Many of the 24 uncommitted black voters in the groups, men and women of ages 25 to 65, were deeply uncomfortable discussing Mr. Buttigieg’s sexual orientation, the memo said, adding that “they felt the mayor was ‘flaunting’ his sexuality by the very mention of having a husband.”

In interviews this weekend, black Democratic Party officials in South Carolina largely said that Mr. Buttigieg’s sexuality was not a concern to them, while voters expressed more divergent views. Yet most party leaders and voters agreed that being a married gay man would cause some discomfort with religious or conservative black Democrats.

Mr. Buttigieg’s sexuality may be a factor with religious and white conservative voters as well, but black Democrats are a focal point because they were critical to Hillary Clinton, Barack Obama and others winning the party nomination in recent years.

“The biggest issue for him is he’s married to a man,” said Phyllis Harris-Drakeford, the Democratic chairwoman of Kershaw County, S.C. “I have no problem with that: You love who you want to love and you have the freedom in this country to do that. But in the South in particular, that’s not well favored.”