Mashrou’ Leila are giants in Lebanon. Walking through Beirut with the band on a warm afternoon, it feels like everyone is staring. We squeeze into a retro diner in the city’s bustling Hamra neighbourhood, and have hardly started talking before two women interrupt for a selfie.

As they celebrate their 10th anniversary, the four-piece are already the Arab world’s biggest indie group. They’re also probably the most successful Arabic-language band internationally, with a European tour lined up and a new compilation featuring collaborations with Róisín Murphy and Hot Chip’s Joe Goddard.

They met in 2008 at the nearby American University of Beirut, a leafy hillside campus tumbling down towards the glittering Mediterranean. They first came to this spot – where today they’re picking over greasy burgers and congealed coleslaw – to drink and calm their nerves before early gigs.

“We didn’t have expectations,” says drummer Carl Gerges in French-accented English. “The band wasn’t meant to last forever.” This was reflected in their name, which means “overnight project”. Yet their early songs, such as Shim El Yasmine (Smell the Jasmine), a tender ballad about abandoning a gay lover for a prescribed marriage, and the Balkan jazz-style hoedown of Raksit Leila, shot them to unexpected stardom.

Their surprise was partly down to the fact that few independent Lebanese musicians had made it big before. There was no national infrastructure to support them. Everything in Mashrou’ Leila’s early years was improvised: they won the opportunity to record their debut album in a radio competition and promoted concerts by spraying graffiti in the alleyways of Beirut. When they were invited to be the first Lebanese band to headline the local Byblos festival, they had to hastily write six new songs to fill their set.

Their appeal is particularly obvious live. Lead singer Hamed Sinno is a flamboyant performer with an electric stage presence, his formidable voice as comfortable soaring as it is flirting with Haig Papazian’s keening violin. As their sound matured into superbly sleek electropop on 2015’s Ibn El Leil, their international profile steadily grew. Yet because of their outspoken support for LGBTQ rights (Sinno is a rare out gay figure in Arab media) they have received more press for their politics than their music.

Sinno finds himself saddled with being a voice for Arabs, Muslims and the Middle Eastern LGBTQ community. What bothers him most is when western media treat the band’s progressive politics as exceptional. “It can’t be that absurd to the western imagination that there are many liberal Arabs inclined towards gender and sexual diversity,” he says hotly. “To write them off because of the oppression of free speech in their countries does everyone an extreme injustice.”

The band’s politics saw them banned – twice – from playing in Jordan. “They said the band is immoral, that we incite a revolutionary feeling in people,” says instrumentalist and composer Firas Abou Fakher. At their biggest concert ever, to 35,000 people in Cairo, the appearance of two rainbow flags in the crowd scandalised the Egyptian press. Rumours spread that the gig had actually been a giant orgy and that the band were in prison. The Egyptian government arrested 75 people that they suspected of being gay in the ensuing crackdown.

The band watched this happen from abroad, powerless. “Our inboxes were constantly littered with death threats and the most hateful remarks possible,” says Sinno, his eyes widening. He becomes uncharacteristically quiet. “It was fucking traumatising.” They also incurred the financial loss of being blocked from performing for their two biggest fanbases. Now looking to a western audience, they have started writing lyrics in English, but Sinno rejects the idea that this makes him less authentic. “There’s something to be said for a band from the Arab world to make it, regardless of language,” he says.

Still, the band won’t abandon their Arabic hits. At gigs abroad they see fans who don’t speak Arabic attempt to sing along with eyes closed and no idea what they’re saying. “In the current political climate, the fact that people could relate Arabic not to Islamic fundamentalism and terror, but to learning phonetics and going to a concert, it’s a kind of political victory,” says Sinno, smiling. “And it’s moving.”