A Russian lesbian family who faced death threats after they appeared in an advertisement for the food chain VkusVill say they feel safe in Barcelona and accepted for who they are.

The family were targeted in a hate campaign on social media after they appeared in the ad. The company later apologised and replaced the photo with one of a heterosexual family.

“We don’t feel safe in Russia because of its homophobic laws,” Mila, the family’s younger daughter, said. “Lots of chatrooms published our Instagram accounts and email addresses. There were a lot of stupid comments but also terrifying ones, like the picture of an axe covered in blood.”

Her mother Yuma and partner Zhenya appeared in the ad with their two daughters under the slogan “recipes for a happy family” but the company quickly withdrew the campaign after receiving a mass of hate mail.

After the firm published an apology, saying that publishing the photograph showed a lack of professionalism on the part of its employees, the family was bombarded with phone calls and hate mail on social media, which included threats to rape Yuma’s eight-year-old granddaughter.

“We don’t have anti-discrimination laws [in Russia] so we don’t have any protection,” Mila said. “We can’t go to the police.”

Mila said the family has no bad feelings towards VkusVill. “It’s just a company in a capitalist country with a homophobic government,” she said. “We’re not angry with them, we’re happy that we were allowed to speak for ourselves and represent our LGBT family because LGBT people in Russia are alone and abandoned by their families. They are afraid and not accepted in society so it was an opportunity for us to say we exist.”

In 2013 Russia passed the “gay propaganda law” which is “aimed at protecting children from information promoting the denial of traditional family values” and bans the “promotion of non-traditional sexual relations to minors” in the press and online.

The law has forced teachers and medical professionals to self-censor what they say about non-traditional families and has been used to shut down websites that provide information and services to young LGBT people across Russia.

“The Spanish newspaper El Pais published a story about us and a lot of people in Spain said we should come and that we would be safe here and that we deserved better,” she said. “Also, people said the LGBT policy is good here and there’s a lot of support.

“We can’t go back under the existing regime because we won’t be safe,” Mila said. “Russia is home, it’s in our hearts, and we want to be with our people but the safety of our family comes first.

“We’re not sure about our future but we feel safe in Barcelona. Here we can be ourselves and live as a normal family. My mother and sister hope to get married here and have children, things we can’t do in Russia.

“We’re happy to show our happiness and to show people in Russia that queer people who don’t have this happiness can see that it can be real.”