Rau's appeal that Islamic headscarves receive equal treatment with symbols of other faiths such as Christianity or Judaism has led to furious reactions from Roman Catholic politicians and clerics.
"State schools must respect each and everyone, whether Christian or pagan, agnostic, Muslim or Jew," Rau said on television.
"If the headscarf is an expression of religious faith, a dress with a missionary character, then that should apply equally to a monk's habit or a crucifix."
If headscarves are banned in German schools, then other religious symbols should get the same treatment, he argued.
This drew an angry retort from Edmund Stoiber, Bavarian state prime minister and head of the ultra-conservative Christian Social Union, the Bavarian wing of the Christian Democratic Union, Germany's main opposition in parliament.
Rau has no right to "cast doubt on our national identity, distinguished by the Christian religion," he said.
He described Islamic headscarves in schools as "a political symbol incompatible with our democracy".
Bavaria is preparing legislation to ban the wearing of Islamic headscarves by teachers while crucifixes continue to adorn classrooms in the strongly Catholic southern German state.
The southwestern state of Baden-Wuerttemberg, dominated by the Christian Democrats, also wants to ban teachers from wearing headscarves while continuing to permit the wearing of Christian or Jewish religious symbols.
"If the headscarf is an expression of religious faith, a dress with a missionary character, then that should apply equally to a monk's habit or a crucifix"
Cardinal Joseph Ratzinger, the German prelate who heads the Vatican's Congregation for the Doctrine of the Faith, criticised what he called the "strange doctrine" of President Rau, himself a devout Protestant believer.
"I will not forbid any Muslim to wear a headscarf, but still less do we accept a ban on wearing the crucifix," he said in a Christmas Eve sermon.
Following the reaction, Rau said that he had not come out either for or against the wearing of headscarves in schools, but had simply appealed for equal treatment of all religions.
Rau, a Social Democrat like Chancellor Gerhard Schroeder, won support from the environmentalist Green Party, a junior partner in Schroeder's left-of-centre coalition.
Schroeder said in an interview last Sunday that he was opposed to public servants wearing headscarves but was not against students wearing them in schools.
The headscarves issue has led to
mass protest in France
Germany's highest tribunal, the federal constitutional court, ruled in September that Baden-Wuerttemberg was wrong to forbid a Muslim female teacher from wearing a headscarf in the classroom.
But the court said individual states could legislate to ban religious apparel if it were deemed to unduly influence children.
Since then, Baden-Wuerttemberg and neighbouring Bavaria have drawn up legislation and plan to put a ban in place.
The issue has also been a hot topic of debate in France.
Ignoring warnings that it would alienate France's five-million-strong Muslim minority, French President Jacques Chirac on Wednesday came out in favour of a ban on headscarves in schools.