Some 58 per cent say bosses should not be allowed to ask them to show their gender pronouns of him, she or they.
And 52 per cent say staff should not be fired for sharing a controversial political belief — if it is expressed out of work time and is not illegal, think tank Policy Exchange found.
Only a fifth of the 1,169 people polled said firms should be able to refuse to do business with customers with whose beliefs they disagree.
Prof Matthew Goodwin, head of the Corporate Culture Wars Project at Policy Exchange, said the poll showed many are “instinctively opposed to firms getting involved in the culture wars”.
He added: “They don’t think companies should be discriminating against workers because they might hold or express particular beliefs.
“They don’t think companies should refuse to do business with people who hold particular views — and they don’t want their employer to be demanding they align themselves with particular political belief systems, such as gender identity theory.”