When asked whether they were personally comfortable with their salaries being made public, 66 percent of respondents said they wanted the information kept private. But when asked about a general workforce release of wage information, opposition increased.

Read: Better pay, better engagement

"There's no doubt that when it comes to publishing wages, most Americans think it's a sensitive topic and a private matter," says Dr. Lee M. Miringoff, director of The Marist College Institute for Public Opinion.

Highlights of the survey included:

• 72 percent opposed the public publishing of salaries by private companies;

• 79 percent of whites opposed it;

• 61 percent of nonwhites opposed it.

What about disclosing such information internally? This is where the gender gap appeared. Again, most folks were opposed to internal disclosure — 73 percent overall.  But men were much more opposed to releasing the data internally than were women, 79 percent compared to 67 percent.

Read: Employers, employees far apart on compensation equity

If companies went ahead and published the information anyway, Marist asked, what would the likely outcome be?

The largest negative factor cited by respondents was it would "cause conflict between employees rather than increasing fairness of pay within the company." That's what 58 percent said. White respondents were much more concerned about that conflict than were nonwhites, with 63 percent choosing "internal conflict" compared to 51 percent.