A group of Batley Grammar School parents have called for calm after a teacher showed students a caricature of the Prophet Mohammed.
The image was shown to children by a teacher in a religious studies class as part of a discussion about blasphemy on 22 March.
It prompted protests outside the school in West Yorkshire, an apology from the school, and the suspension of the teacher involved.
Depictions of Mohammed are considered offensive to Muslims.
On Sunday evening, Yunus Lunat, spokesperson for the Batley Parents And Community Partnership, said the teacher had failed to realise the image was "loaded with Islamophobic tropes".
He added: "We believe that in a democratic society everyone holds a right to opinion and expression, however, we as parents and citizens also believe that with these rights come responsibility.
"We as parents and citizens stand resolute that our children should be able to attend school without having their faith – which is protected in law – or their culture ridiculed, insulted or vilified."
Police had been called to the school on Thursday and Friday, as protesters called for the teacher involved to be sacked. There have been no arrests.
Mr Lunat had expressed fears last week that the incident would be "hijacked" by those who are anti-Muslim, a concern echoed by Labour MP for Batley and Spen Tracy Brabin, who had accused people of "fanning the flames" in a way that would "only provoke hate and division".
On Sunday evening, Mr Lunat said: "Unfortunately, unhelpful comments and biased media reporting that seek to hijack the issue have undermined the essential relationship between local communities and local public institutions.
"We are fully invested in dialogue and legitimate engagement.
"Any and all such threats against the school and staff involved undermine our efforts and are completely contrary to our values as concerned parents, citizens and Muslims.
"We therefore call for calm in order to allow for fruitful dialogue and space for a transparent investigation to be undertaken."
He said children should be allowed to "engage with challenging ideas such as blasphemy without their teachers having to resort to using Islamophobic material" which "only serves to marginalise Muslim communities and spread Islamophobic sentiment".
Parents were grateful for the school’s cooperation so far, he said, adding that "initial progress" had been made, with the school removing the caricature of Mohammed from its material and also announcing a review of the religious studies curriculum.
The school’s head teacher, Gary Kibble, had said on Thursday: "The school unequivocally apologises for using a totally inappropriate image in a recent religious studies lesson. It should not have been used.
"A member of staff has also relayed their most sincere apologies. We have immediately withdrawn teaching on this part of the course and we are reviewing how we go forward with the support of all our communities represented in our school.
"It is important for children to learn about faiths and beliefs, but this must be done in a respectful, sensitive way."
A spokesperson for the Department for Education had said: "Schools are free to include a full range of issues, ideas and materials in their curriculum, including where they are challenging or controversial, subject to their obligations to ensure political balance.
"They must balance this with the need to promote respect and tolerance between people of different faiths and beliefs, including in deciding which materials to use in the classroom."