According to a new Harris poll released Thursday, two-thirds of Americans support federal legislation that would bar employers from discriminating against workers on the basis of sexual orientation and gender identity, and 55 percent reject exemptions for any employers -- even churches.

The online survey, conducted Sept. 10-18 with Out & Equal Workplace Advocates and Witeck Communications, found that only 35 percent of Americans think religious organizations are legally justified to discriminate against lesbian, gay, bisexual and transgender workers on faith-based grounds. Slightly fewer respondents, 30 percent, made the same exception for privately held businesses. About 1 in 5 Americans said publicly held businesses should be able to claim a religious exemption as well, according to the survey, which interviewed 2,543 adults in the United States.

In July, President Barack Obama issued an executive order protecting LGBT employees of federal contractors and the federal government from employment discrimination. The provision pertaining to federal contractors, which does not grant any exemptions for religiously affiliated contractors, affects 24,000 companies employing nearly one-fifth of the U.S. workforce. But in 29 states, all other workers can still be legally fired or harassed for being gay, lesbian or bisexual. For transgender employees, that's true in 32 states.

In Congress, legislation to remedy this gap has passed the Senate but stalled in the GOP-controlled House. The Employment Non-Discrimination Act, which would protect all LGBT workers from workplace discrimination, has also lost support from a number of gay rights groups in recent months because of its inclusion of a wide-reaching religious exemption that would give faith-affiliated businesses legal cover to discriminate against LGBT employees.