About 4 of 10 LGBTQ workers say they aren't fully "out" at work, according to a new study from jobs website Glassdoor.

Half of those surveyed said they feared being out would hurt their career prospects, from getting passed over for a promotion to even losing their jobs.

More than 5 of 10 LGBTQ workers said they had experienced or witnessed anti-LGBTQ comments from co-workers.

One of the most rapid social shifts in recent decades is the acceptance of LGBTQ people, from gay marriage to television shows featuring transgender and gay characters. But LGBTQ workers say they're not always feeling the love in their workplaces.

Slightly more than 4 of 10 LGBTQ workers say they aren't fully "out" at work, according to a new survey from employment site Glassdoor, which undertook the survey in advance of Pride Month in June. The reasons for worker reluctance may boil down to fears about bias and discrimination, with about half of those surveyed saying they believe being out in the workplace could hurt their careers.

The findings underscore the fears and concerns many LGBTQ people continue to feel in the workplace, especially at a time when some state lawmakers are sponsoring bills that would limit the rights of LGBTQ people, such as a rash of "bathroom bills" sponsored during the past few years aimed at transgender people.

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But the benefits of coming out at work can provide a productivity boost both to LGBTQ workers and their employers, with Australian researchers finding in earlier surveys that "out" workers are more satisfied and happier in their employment.

The latest findings are a "wake-up call," said Scott Dobroski, senior director of corporate communications at Glassdoor and a member of the LGBTQ community. "I was a little surprised and disappointed and it makes me sad, honestly, that nearly half of LGBTQ workers believe that being out at work could hurt their careers."

But, he added, he wasn't surprised that more than half had experienced anti-LGBTQ comments at work, since he noted he's among those who have been at the end of a negative comment. "It's a mixture of intentional and unintentional comments that can occur," he said. "What it illustrates is there is a continued need for education about what is appropriate in the workplace for any minority group."

Workers who are LGBTQ -- which most often stands for lesbian, gay, bisexual, transgender and queer or questioning -- aren't always guaranteed workplace protections, another concern for some employees. Twenty-six states don't provide legal protections for LGBTQ workers, Glassdoor noted.

More employer support wanted

Despite the seachange in public support for gay rights, employers need to do more to support LGBTQ workers, the survey respondents told Glassdoor. It's not enough for employers to march or support in a Pride parade, for instance, Dobroski noted. Instead, LGBTQ workers are looking for policies that show support for their community, such as extending the same benefits to LGBTQ workers as to straight employees, like parental leave, Dobroski added.

Lawsuits alleging discrimination for anti-gay bias aren't uncommon. In April, the Supreme Court took a case that could determine whether companies can fire workers for their LGBTQ identities, with two of the plaintiffs claiming they lost their jobs because they were transgender and gay, respectively.

But even companies aiming to be supportive of LGBTQ workers may be falling short. Employment experts say creating an inclusive workplace should include examining diversity policies to make sure they support LGBTQ parents and people who are transitioning, for example. Other steps include providing gender neutral bathrooms and work forms with options for people who don't identify as either male and female, the Australian researchers wrote in the Harvard Business Review.

"Employers want to fuel their businesses for financial success, and you need quality talent to do that," Dobroski said. If they don't show support to the LGBTQ community, "their companies are missing out on great talent."