A survey in America has found that an overwhelming number of LGBT people say society has become more accepting, despite 4 in ten people having experienced rejection from a friend or family member because of their identity.

The Pew Research Center conducted a survey of 1,197 LGBT Americans, asking an in-depth range of questions.

An overwhelming 92% of respondents said society had become more accepting of LGBT people in the past decade, and expected more progress in the next  ten years. Pew Research claims this is linked to more people being out about their sexuality or gender identity, meaning more people know someone who is LGBT.

However, LGBT individuals still faced stigmatisation. Almost four in 10 (39%) reported that they had faced rejection from a friend or family member after coming out to them. 21% had been discriminated against at work, 30% had been attacked or threatened physically, and 58% had been the target of homophobic or transphobic slurs.

This may partially account for why fewer LGBT Americans polled as being “very happy” with their lives – compared to 30% of people in general.

“What we find is that for LGBT Americans, these are the best of times, but that doesn’t mean these are easy times,” said Paul Taylor, the Pew Center’s executive vice-president. “Many are still searching for a comfortable place in a society where acceptance is growing but remains limited.”

The survey also discussed what people consider the most important issues in LGBT rights are.

With the Supreme Court poised to rule on two crucial equal marriage decisions on Monday, 93% of respondents said they supported legalisation of same-sex marriage, but many felt there were more important issues receiving far less coverage.

HIV prevention and workplace discrimination were major concerns for many respondents. Employment discrimination, in particular, is a stumbling block in the US, which has no national laws against firing someone for their sexuality or gender identity.

Yesterday President Barack Obama urged Congress to pass the Employment Non-Discrimination Act (ENDA), which would prohibit businesses from discriminating against LGBT people. Lawmakers have attempted and failed to pass ENDA in almost every Congress since 1994.

“There’s clear evidence that people were at least as concerned about employment discrimination as they were about marriage equality,” said advisor Gary Gates. He added that deciding on priorities was “an ongoing struggle in the LGBT movement.”

Most of the respondents to the survey were bisexual, yet the survey found they were far less likely to be out than gay people. While 77% of gay men and 71% of lesbians said they were out to friends and family, the same was true for just 28% of bisexual people.

Asked which public figure contributed most to progress in LGBT rights, 23% of respondents named President Obama.

18% chose lesbian talk show host Ellen DeGeneres, while gay journalist Anderson Cooper and Secretary of State Hilary Clinton also gathered smaller numbers of votes (less than 3%).

A Pew Research report released in May found that support for equal marriage is most common among Americans born since 1980, with 7 in 10 in favour of legalisation.