It is debatable that the Finzi Continis really live in such isolation through the whole novel. It is true that they are introduced as a family that lives apart from the Jewish community and from the town of Ferrara as a whole. Their mansion is surrounded by gates and walls, they use a different synagogues and don't go where the majority of Jews go, the children Alberto and Micol do not go to state school but are privately tutored. The nameless narrator, who is involved in the events of the novel, describes them as elusive and mysterious. The narrator's father goes as far as defining them with the paradox of aristocratic anti-Semites.
Yet, in the course of the novel, the family does open its mansion to the outside world. The Jews who have been banned by the tennis club as the result of the racial laws in 1938 are invited by the Finzi Continis to play in their courts. This creates a world apart from the pervasive racism that is sweeping Ferrara (a microcosm for Italy as a whole and for Europe). This world, however, proves ephemeral as the Fascist persecution of Jews tightens its grip. In this respect too, the Finzi Continis are just like all the other Jews. What the future holds for them is deportation and an anonymous death in a concentration camp, the fate of millions of Jews during Fascism and Nazism.
They live apart as a show of status and because they are unwilling to take a great role in the "too italianized" jew community.
They live in a false sense of security when tragedy is looming over them, because these walls will not protect them.
But it's not correct to say that they don't see the danger coming. Still, they don't flee, but it's exactly the same behaviour as the majority of jew community.