SALT LAKE CITY — While finding that Americans narrowly favor allowing gay and lesbian couples to legally marry, a new Associated Press-GfK poll also shows most believe wedding-related businesses should be allowed to deny service to same-sex couples for religious reasons.

Roughly half the country also thinks local officials and judges with religious objections ought to be exempt from any requirement that they issue marriage licenses to gay and lesbian couples, according to the poll.

That view of the same-sex marriage issue echoes that of the Mormon church. Last week, the church called on state legislatures to pass new laws that protect gay, lesbian, bisexual and transgender people from discrimination but also to protect the rights of those who assert their religious beliefs.

David Kenney, a self-employed Catholic from Novi, Michigan, said he’s fine with same-sex marriage being legal. He’s among the 57 percent of Americans who said wedding-related businesses — such as florists — should be allowed to refuse service if they have an objection rooted in their religion.

“Why make an issue out of one florist when there are probably thousands of florists?” asked Kenney, 59. “The gay community wants people to understand their position, but at the same time, they don’t want to understand other people’s religious convictions. It’s a two-way street.”