More than half of Republican voters in a new Hill-HarrisX poll said that adoption agencies should not be allowed to refuse service to same-sex couples.

The nationwide survey released on Tuesday showed that 66 percent of Republicans said that adoption groups should not be able to turn away LGBTQ parents, compared to 75 percent of Democrats and 73 percent of independents.

Overall, a vast majority of voters shared this sentiment: 72 percent said that adoption agencies should not be allowed to deny service to members of the LGBTQ community, while 29 percent disagreed.

The survey follows a new Department of Health and Human Services adoption rule announced earlier this month.

The proposal seeks to roll back Obama-era protections that expanded anti-discrimination protections to include sexual orientation. It effectively allows federally funded adoption groups to reject LGBTQ parents on the basis of religious beliefs.

While some religious groups have praised the rule, a number of LGBTQ groups have condemned it.

Human Rights Campaign President Alphonso David said the change gives faith-based adoption groups a “blanket license to discriminate.”

“What this rule will allow these agencies to do is to discriminate in a blanket fashion,” he told Hill.TV. “It’s essentially saying, ‘I’m not going to allow adoption-related services to any families unless they’re Christian-based families.’ ”

In pushing back against criticism over the proposal, White House deputy press secretary Judd Deere maintained earlier this month that “LGBT people can still adopt and that will not change.”

“The federal government should not be in the business of forcing child welfare providers to choose between helping children and their faith,” Deere told The Hill.

The Hill-HarrisX poll was conducted online between Nov. 8 and Nov. 9. It has a margin of sampling error of 3.1 percentage points. The sampling error among partisan voters is higher.

—Tess Bonn