Florence is known to Italians as a city that is visited by hundreds of thousands each year, but which even people from other parts of Italy who have lived there for decades say will never be home. Florentine frigidity is magnified in the case of non-Italians, especially non-white migrants – those still referred to pejoratively as extracommunitari, undesirable nationals from outside the European Union.

Racism and marginalisation are not unique to Florence. Italians have found it hard to accept the fact that there are now 5 million immigrants – or 10% of the workforce – in the country. There is a strong feeling, reinforced by the haphazardness of policies on migration, asylum and "integration", that this migration may still be temporary or transitory, that it cannot possibly transform Italian culture, politics or society in any deep sense.

Italy is not Britain, France or Germany. The memory of its colonial past goes almost universally unacknowledged, or even unknown, and its fascist past is treated either as an aberration or as a more benign version, more focused on societal discipline and patriotism than on exclusion and genocide.

Against this backdrop, the killings of two Senegalese men, Modou Samb, aged 40, and Mor Diop, aged 54, and the injuring of three others on Tuesday by Gianluca Casseri, 50, a local man with far-right allegiances, should perhaps not come as a complete surprise. Casseri's profile certainly fits the stereotype of the lone gunman. After going on his shooting spree, armed with a .357 Magnum, killing Samb and Diop in the suburban Piazza Dalmazia and going on to shoot three others in the central market of San Lorenzo, Casseri shot himself. He is described as a fantasist, an author of cult essays and books inspired by Tolkien and Evola, who dreamed of a return to the pagan roots of a Europe reigned over by Norse kings.

The motivation for the killings has focused on Casseri's affiliation with the rightwing CasaPound organisation, a non-conformist social movement that came on the scene in 2003, mirroring the outlook of the autonomous left – squats, social centres, music and fanzines, attacks on neoliberalism, the state and the police – but for white Italians only.

Pap Diaw, the veteran leader of the Senegalese community in Florence, has called for the organisation to be shut down following the murders. CasaPound has distanced itself from Casseri, claiming that while he may have frequented the organisation, he was no key activist. In response, Partito Democratico member Emanuele Fiano asked why CasaPound had been busy removing Casseri's articles from its website as the news emerged.

CasaPound and majority opinion are united in dismissing Casseri as a deranged loner. However, as the experiences of migrants testifies, Casseri is the symptom of a racism that is deeply ingrained in Italy. The precariousness of the lives of vendors such as the two victims – "illegal" migrants with no possibility of regularisation, living hand-to-mouth, at the mercy of the police, the extreme right and the local population, who patronise them at best, abuse them at worst – is endemic.

The fact that police set upon marchers protesting against the killings on Tuesday, and arrested tens of Senegalese men, reveals the extent to which black people in Italy are seen as having no legitimacy to speak out about the injustice they face. Nor were the shootings an isolated incident. On 11 December, a mob descended on the Continassa camp in Turin, home to Roma migrants. The camp was burned to the ground and cleared of all its residents following the false claim by a 16-year-old girl that she had been raped by two Roma men – an allegation she later admitted had been made up.

Nevertheless, migrants in Italy are speaking out. Migrant activists, tired of the state's empty promises of integration and citizenship, and of the anti-racist left's paternalism, are taking action. Organisations such as the Self-Organised Immigrants' Collective, the Senegalese Association and the Movement of Asylum Seekers signed a statement calling for the Turin arson and the Florence killings to be seen as the "tip of the iceberg against a cultural and social backdrop fuelled by norms such as the [anti-immigration] Bossi-Fini law, the (in)security pact, and municipal policies against street vendors, Roma and windscreen cleaners, etc".

As Pap Diaw says, the murderers and arsonists of Florence and Turin "profit from a toxic climate to carry out these barbaric acts". The deaths of Samb and Diop are the symptom of a Europe whose racism does not even try to disguise itself. It is the indignity in which migrants are forced to live in a systematically racist continent, and not just the ideology of the extreme right, that needs to be scrutinised if more senseless deaths are to be avoided in the austere Europe of the coming decades.