A new study suggests that while school and college staff are largely confident about their duties under the Prevent initiative, there are fears about the impact on certain groups of youngsters.
It also reveals there is "discomfort" about the requirement to promote fundamental British values, such as tolerance and democracy, particularly the labelling of these values as "British".
The Prevent strategy, introduced two years ago, requires authorities such as schools, colleges, prisons and health professionals to refer any concerns or suspicions they have about individuals as part of attempts to stop people being radicalised and drawn into terrorism.
The initiative covers all forms of extremism, such as far-right or Islamist.
The small-scale study by the universities of Coventry, Durham and Huddersfield was based on in-depth interviews with about 70 education professionals across 14 schools in West Yorkshire and London, and eight council-level Prevent workers, as well as a national poll of 225 school and college staff.
It found that, in general, there was no widespread opposition to Prevent, with staff feeling confident about their responsibilities to refer any concerns, understanding it is part of school or college safeguarding duties.
There were concerns that Prevent can make Muslim students feel "singled out".
"We found widespread - and in some cases very acute - concerns about increased stigmatisation of Muslim students," the study says, adding that many of those interviewed also said they and their colleagues were working to ensure the duty does not have an effect in students.
It also says a small number of those questioned argued the responsibilities put on schools and colleges by Prevent "might, in fact, be counter-productive to the prevention of extremism - either because they might lead to Muslim students withdrawing from sharing concerns and questions with staff due to feelings that they are being singled out for more attention and scrutiny, or because they might more generally stoke feelings of being marginalised by the state and society".
In terms of British values, the study says: "We found widespread discomfort and uncertainty around the focus on the specifically British nature and content of these values."
Lead researcher Dr Joel Busher, of Coventry University, said: "Approaching Prevent as part of safeguarding appears largely to have been accepted by schools and colleges, and has helped to foster fairly widespread confidence about the duty.
"However, linking the duty to the promotion of 'fundamental British values' - and in particular the pressure on schools and colleges to emphasise the 'Britishness' of these values - is often seen as more problematic."
He added: "Widespread and sometimes acute concerns about possible feelings of stigmatisation among Muslim students highlight an urgent need for systematic evaluation of how, if at all, the Prevent duty has impacted on student experiences."