Last year, it had to delay the release of its anti-homophobia video, because it couldn't find a footballer to back the message, publicly.
Anton's father, Glenn, knows about English football.
Before the 1989/90 season, he signed for Liverpool, and - according to the Independent newspaper, in October 1989 - was a "defender of such class and distinction...
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As it happens, this was just a year before Justin Fashanu became the only English player to come out.
Later, after his career had ended, Fashanu hanged himself. But I've told Anton, just to forget it." There hasn't been any trouble so far.
Glenn is still heavily involved in the game, as a commentator and as a coach at Utsiktens. He's fatalistic about the abuse which may yet be hurled at his family. "But they will come." He, his other football-playing son, and Anton may all be targets. Crowds are small, as the teams are still playing only warm-up games, at the end of the long winter break.
His sexuality should not, Anton, asserts be "a big thing". The reason is that of all the professional footballers playing among Uefa's member associations - let alone those playing in other countries around the world - there appears to be no other avowedly gay player.
The Guardian newspaper's "Secret Footballer" (its anonymous Premier League-playing columnist) says that "the changing room is a very harsh place to survive", but intimates that the banter would not be any worse for a player because of his sexuality, as opposed to, say, his haircut. Niklas Tidstrand plays alongside Anton in midfield, and is a friend.
He says half the team knew even before Anton came out in public, but still it's been tough. "Because there are so many jokes about 'playing like a man'." And there's the very rarity of it. When we started to talk about this, maybe two years ago, we searched on Google for "gay football players" - and nothing, nothing, it's just jokes. So many are gay, but no-one wants to say before their career is over." And the reason for that was laid bare in the campaign organised by the English FA.
It's stolid, self-confident, quiet and handsome - rather like the inhabitants. Because Sweden's second city harbours a global one-off. Anton Hysen is the sprightly 20-year-old left-sided midfielder for Utsiktens BK, a team from the fourth tier of the Swedish league.
He has gelled hair, a collection of piercings, and the names of his parents tattooed in large, cursive font along his forearms.
He also - after a polite enquiry by the Swedish football magazine Offside - came out earlier in March. In their bright, white living room, Anton is spooning a vat of pasta and meatballs into his mouth, before he heads off to Monday night training. But as Anton wanders into the kitchen to collect his dessert, she also says that she's worried. "He was stabbed for being gay." She is talking of Peter Karlsson, murdered in 1995 by a Swedish neo-Nazi. He's been inundated with gifts, messages of support, and invitations to swanky events.
He exudes quiet self-assurance: "I'm sure of who I am," he says. I have nothing to hide." He was surprised, he says, about what a stir - globally - his announcement caused. "Just because I'm gay doesn't mean I want to go," he says of the latest request.