The move comes just days after the Church of England announced that any member of the clergy found to be a member of the far-right organisations would be defrocked.
Delegates at the AGM of the EIS heard that there were already provisions to ban teachers who expressed racist views in the classroom.
However, the union decided to campaign on the issue by calling on the Scottish Government to ensure members of the BNP, led by Nick Griffin, below, and other fascist groups would not be allowed to teach in schools.
Charles McKinnon, from the union's Glasgow local association, said: "People who hold those views should not be anywhere near a classroom because they cannot just dump their racist baggage at the school gate.
"We don't allow BNP members to be police officers or prison officers so how can it be acceptable to allow them to be responsible for the education of young people?"