By explicitly noting that the employers have religious or moral grounds for objecting to the mandate, the question elicits a radically different response.

The Pew question already mentions “religious reasons,” but framing can still make a difference. It’s one thing for a respondent to be against letting businesses “refuse to serve same-sex couples.” It’s another thing to say people shouldn’t be allowed to “decline to participate in a same-sex wedding.” The former evokes the image of a restauranteur or shopkeeper throwing gay people out of his business, while the latter sounds more like he’s politely reserving the right not to take someone on as a new client. The end result might be the same, but the connotations are worlds apart.

The most likely explanation is that a lot of people see this as an issue marked by shades of gray. They don’t believe it’s OK to discriminate against gay couples and would hate for anyone to mistake them for a homophobe. But they’re also inclined to want others’ religious beliefs respected, and heavy-handed government rubs them the wrong way too. So they sit somewhere in the middle, unsure how these considerations ought to be balanced against each other—and ultimately answer poll questions mostly based on how the wording makes them feel.