It follows controversies such as 2021 protests against a teacher in Batley, West Yorkshire, who received death threats and went into hiding after showing pupils a cartoon of the Prophet Muhammad from Charlie Hebdo, the French satirical magazine, during a religious studies lesson.
Similar concerns over the right to freedom of expression and protest have been raised in the aftermath of the October 7 2023 Hamas terror attack on Israel and the ensuing Gaza conflict.
More than a third (36%) felt they had to hold back on expressing their views on race or ethnicity, while 32% said they did not feel they could freely speak out on immigration or religious extremism.
On asylum and Gaza, 31% felt constrained, rising to 41% for transgender issues.
Groups that were predominantly white, male, older, and non-graduate were more strongly in favour of free speech, regardless of the issue, but at the same time felt more constrained in their ability to freely share their views about most topics.
Nearly half of this group (48%) said they felt they had to restrain their comments on race, far higher than the average of 36%. The same was true on immigration, where 43% felt they had to hold back on their views compared to an overall average among the public of 32% who felt constrained.
Christians were more likely to back the right to free speech, but also more likely than average to feel they had to hold back on expressing their views.
Conversely, women, younger Britons, and people from ethnic minorities or non-Christian religions tended to think that people needed to be more sensitive in the way they spoke.
Just under a third (29%) of all those polled agreed that people needed to be more sensitive. But this rose to 34% amongst women, 45% from ethnic minorities and 45% for non-Christians.
By contrast, men, people aged over 65, those from white ethnicities, and Christians were more likely to think that people are too easily offended.
While on average 49% felt people were too easily offended, this rose to 56% of men, 54% of those from a white ethnicity and 59% for Christians. These were nearly double the rates for people from ethnic minorities and non-Christians.
Race and ethnicity was the only topic overall where the balance of opinion was more towards avoiding offence rather than speaking freely (by 42% to 34% ), according to the research.
People predominantly held back from expressing their views to avoid causing offence or starting an argument.
Forty-six per cent resisted expressing their views on any religious figure, text, or teaching and just 35% held back their political views to avoid causing offence.
Some said they held back because of heightened concerns about their safety. For religious topics, 25% said they restrained themselves because of safety fears, and 17% over political views.
The report said there was a group of people for whom free speech was a significant issue. They represented about 37% of the total sample and were described by researchers as those who were most concerned about the pace of change.
But they were also the group most likely to express “heightened concerns” about their ability to speak freely about race, immigration, asylum, and religious extremism.
Robert Jenrick, the shadow justice secretary, said: “The left’s determination to shut down debate around immigration has created a chilling environment for free speech. In this context, a catch-all definition of Islamophobia would be a disaster, worsening the culture of fear that has spread throughout society.”