Support for same-sex relationships is rising sharply among all major ethnic and racial groups and most religious groups, according to a major new survey.

The American Values Atlas, conducted by the nonpartisan, nonprofit Public Religion Research Institute, comes as the Supreme Court is considering whether a Colorado baker may legally refuse to make a cake for a same-sex wedding on First Amendment grounds.

The survey found a dramatic increase in support for same-sex marriage across all racial and ethnic groups and almost all religious groups just since 2013. More than 6 in 10 — 61 percent — of Americans say same-sex couples should be able to marry legally, compared with 30 percent who are opposed. Five years ago, support was at a bare majority of 52 percent.

The survey — one of the most extensive of its kind, questioning more than 40,000 Americans in weekly installments for eight months last year — focused on issues of importance to the LGBTQ community, including same-sex marriage and protections against discrimination in housing, public accommodations and employment.

The Public Religion Research Institute found that supporters of same-sex marriage now make up majorities among Democrats and Republicans; blacks, whites and Latinos; Catholics; and most white mainline Protestant denominations.

Notably, opinions among black Americans have shifted from opposition — 41 percent supported same-sex marriage in 2013 — to support, with 52 percent signaling approval, the survey reported. Opposition among black Protestants has shifted especially strongly, falling from 57 percent in 2013 to just 43 percent, it said.

"The country has reached a milestone moment in the debate over LGBT rights," said Dan Cox, the institute's research director. "At a time when Americans are more divided than ever, the sea change in support for LGBT rights that now crosses lines of race, ethnicity, religion and geography means that LGBT rights are becoming one of the few areas of public agreement."