Conducted by fan-opinion platform Forza Football and campaign group Stonewall, the survey asked more than 50,000 supporters in 38 countries about their attitudes towards inclusion and homophobia.
Equal rights campaigners hope the World Cup in Russia next year and the following tournament in Qatar in 2022 will be a chance to raise the issue of lesbian, gay, bisexual and trans (LGBT) rights in the two countries.
Overall, 76 percent of respondents said they would be comfortable with a player from their national team coming out as gay or bisexual, with nearly nine of 10 fans in Iceland and Ireland expressing this view.
At the other end of the spectrum, in the United Arab Emirates, Saudi Arabia and Egypt, only around one in 10 fans feels the same way.
The figure for Russia is nearly one in two, but just 14 percent of fans in Qatar said they would be happy with an LGBT player in their national side.
Homosexuality was decriminalised in Russia in 1993 but prejudice is common and human rights activists allege widespread abuse. It is illegal in Qatar.
The highest-profile European footballer to come out is former German international Thomas Hitzlsperger, who played in England and Germany, but he only made his announcement in 2014 once he had ended his career.
“We believe the upcoming World Cups are an opportunity to shine a light on what the situation is like for LGBT people in Russia and Qatar and start conversations that can lead to positive change,” said Stonewall chief executive Ruth Hunt.
The poll shows changes in attitudes since it was first carried out in 2014, when only one in five Russians said they would be comfortable with a gay or bisexual player.
When asked if football’s world governing body FIFA should consider LGBT issues when awarding the rights to host a tournament, nearly two-thirds of fans worldwide agreed but just one in four Russians and one in seven Qataris said it should be a factor.
Patrik Arnesson, the chief executive of Forza Football, said: “Lesbian, gay, bi and trans people are part of the football community across the world and have as much right to play, watch and follow the game as much as anyone else.
“Organisations like FIFA and national leagues and governing bodies have a responsibility to ensure that fans across the world are educated about the importance of welcoming LGBT players and fans, and they must challenge discrimination and abuse at their tournaments.”
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