A trade union representing teachers reportedly donated £3,000 to the Purpose of Life charity, which is involving in protests outside Batley Grammar School.
Earlier this month a religious education, who is in his late 20s, was suspended by the school after parents complained about the lesson in which the cartoon was shown.
The school issued a statement offering an apology to parents whose children study at the state school, where the vast majority of pupils are from minority ethnic groups.
The Daily Telegraph reports that the National Education Union's Kirklees branch, in West Yorkshire, donated £3,000 to Purpose of Life, who later published the teacher's name online.
The Islamic charity has been accused of “endangering his safety” and has been reported to the Charity Commission.
The teacher has received death threats and there have been fears he would end up like Samuel Paty, the French teacher who was beheaded after discussing the cartoon in a lesson last year.
Dr Paul Stott, from the Henry Jackson Society told the Telegraph: “That the Kirklees branch of the NEU has funded an organisation that calls for the sacking of a schoolteacher for doing his job is lamentable.”
Religious education at schools has become a topic of increased attention following the beheading of a French history teacher last October.
Samuel Paty was murdered on October 16 in Paris outskirts after he showed religious caricatures depicting Islamic prophet Muhammad to his students as part of freedom of speech discussion, prompting outrage among their Muslim parents.