This blog posting by the Rev. Ronald Franco, Pastor of Immaculate Conception Parish in Knoxville, Tennessee is an excellent explanation of the use of the crucifix in classrooms in modern day Italy:
This was so despite the fact that the reigning house of the new Kingdom of Italy, the House of Savoy (one of the oldest royal houses in Europe) had a long history of devotion to the Church (and was – until King Umberto II’s death in 1983 – the owner of the holy relic, the Shroud of Turin). The bad blood between Italy and the Holy See would only escalate, of course, after Italy’s conquest of Rome from the Pope in 1870, reducing the Pope-King to a "Prisoner of the Vatican."