WASHINGTON — Weeks after Democrats assumed control of the House with the most diverse class ever, the leaders of their campaign arm invited more than a dozen top political consultants to lead a discussion on the message for their fragile majority. Every one of the strategists was white.

Five months later, House Democrats are reckoning with the same identity politics and hunger for diversity that helped deliver them control of the chamber in November. Concerns about a lack of people of color in critical roles at the campaign arm, the Democratic Congressional Campaign Committee, prompted a huge shake-up this week and an intense scramble to include more minority staff members at the top echelons of the organization.

But that shake-up comes at a cost: The first casualty of the committee’s purge was its executive director, Allison Jaslow, a gay white woman and Iraq war veteran who was a compelling face for swing-district Democrats just starting their first re-election campaigns. The longer-term fallout may be for Representative Cheri Bustos of Illinois, the campaign committee’s chairwoman from Trump country, viewed as a rising Democratic star who had cracked the code on appealing to white working-class voters.

The turmoil reflects an incongruous reality for a party whose backbone of support comes from minority voters in solidly Democratic areas all over the country, but whose House majority rests on a few dozen largely white districts that voted for President Trump in 2016. Even as the Democratic caucus’s liberal brand has been defined by progressive young stars representing diverse constituencies, its path to a lasting majority relies on the success of a new crop of moderates.