The warning came at a gathering of academics and teachers to discuss the role of education in tackling terrorism and religious extremism, against a background of bomb plots and attempted terrorist attacks in the UK.
James Arthur, professor of education at Canterbury Christ Church University and a former member of the Qualifications and Curriculum Authority's citizenship working party, which advises the Government on the curriculum, said religion made many teachers feel so uncomfortable they avoided it.
Speaking at the conference at Roehampton University, he described Professor Bernard Crick, the founding father of citizenship, as a "hard-core secularist".
Government committees on citizenship education were so dominated by people with secular beliefs that religious groups found it difficult to get involved, he said.
"The way teachers are educated, especially in citizenship, is terribly secular," he added.
"There is a tendency for them not to engage with religious ideas. I believe is not because they do not want to engage with religion, but because it makes them feel uncomfortable."
"Teachers are not teaching the whole curriculum. The religious element is there, but it is not being addressed."
He also criticised the teaching of religious education which, he said, had become more like sociology.
Chris Waller, professional officer at the Association for Citizenship Teaching, said citizenship teachers were mindful of their responsibility not to exclude those with religious beliefs from debates in the classroom. But he agreed the lack of teachers trained to teach citizenship may have led to reticence about discussing religion.
Mr Waller said: "The risks for teachers who have not been trained in citizenship could appear daunting. Holding a discussion about Muslim extremism in a city like Bradford would require skill."
Karl Sweeney, head of social studies at Ivybridge community college in Devon, said citizenship teachers needed to tackle controversial issues head-on.
"At our school, we look at what the word fundamentalism means in the context of Islam and Christianity and we talk about the ways they stifle debate and insist people are totally committed to the cause," he said.