WASHINGTON — A move by House Democratic leaders to thwart party members from mounting primary challenges to incumbents, even in safe Democratic districts, could have the unintended consequence of arresting the party’s shift toward a more female and racially diverse caucus, one of its most striking achievements of the last election.

Last week, a Democratic political consultant with longstanding ties to the party’s campaign committees quit a senior-partner position at the firm Deliver Strategies after it, like most dominant campaign outfits, agreed to comply with a Democratic Congressional Campaign Committee policy barring it from conducting business with a primary opponent of a sitting Democrat.

Her reason: She feared the policy’s impact on female challengers.

“It is hard enough for challengers, for a lot of reasons,” said the consultant, Amy Pritchard, who worked last year for Representative Ayanna Pressley, Democrat of Massachusetts, in her successful campaign to defeat a 10-term Democratic incumbent. “And this policy is a bridge too far. I’d like to see a majority of women in Congress, and it’s not going to happen with this policy.”

The D.C.C.C. is ostensibly out to protect sitting Democrats from having to worry about primaries, and instead focus their energy and money on fighting off Republicans. Some female and minority candidates did well in open primaries and beat Republican incumbents last year, even in majority-white districts. They will benefit from the new policy, even as many of them are critical of it.