Speaking anonymously, the elected member, who's been helping party colleagues on the campaign trail ahead of next month's local elections, said that the 2016 murder of Batley and Birstall MP Jo Cox was on the minds of some councillors.
It follows remarks made by a Wakefield Council officer on Monday that some candidates were reluctant to campaign in the current political climate, because they feared for their safety.
Vince Macklam said that the issue was one of the authority's biggest concerns related to Brexit, while the Local Government Association said the "proliferation" of social media was partly to blame for the intimidation of people in public life.
And speaking on Tuesday, one councillor, whose seat is not being contested this year, said she had not been physically harmed or threatened, but feared it may be a possibility.
She said: "In the current climate we are all afraid, deep down, of getting hurt.
"After what happened to Jo Cox it is in people's minds, especially when you’re a woman and you’re going out on your own.
"A lot of people have said to us they're not going to vote at all because of Brexit. Trying to get through the message that Brexit is nothing to do with us is quite hard.
"We have had a couple of angry people waving leaflets at us and saying, "You're rubbish," but luckily it's not been any nastier than that.
"There was one chap on an estate we went round who was very aggressive, but he was one of out of thousands of people, so it didn't bother me too much."
Another candidate, who's standing in the Five Towns area, said he'd been the subject of "three serious incidents in the previous three days" while out canvassing. He said he'd contacted the police as a result.
He explained: "One person said they would throw a brick through my window if I put another leaflet through their door and I’ve also been called a traitor in the street.
“It’s been quite awful.
“I joined my party in 2016 and I’ve campaigned in other parts of the country but I’ve never experienced anything like this.
“It’s understandable that feelings are strong because of Brexit, but that’s not an excuse for this.”
Another councillor standing for re-election said he'd had abuse from voters and on social media.
He said: "Compared to last year and the year before, the mood has been very hostile.
"I wouldn't say I've been threatened, but people have used some very threatening language. On one occasion, a woman leaned out the window and was literally screaming at me to get back down the footpath.
"I understand that people are angry with politicians and they've got every right to express their view, but there's not a lot we can do about Brexit.
"I wouldn't say I feel intimidated going out and canvassing, but certainly some of the people I go out with are. And I'm more wary about going out by myself."
Other local representatives said that they'd had no more abuse than in previous years on the doorstep, while other candidates said difficult conversations with voters were par for the course.
One senior councillor standing for re-election said: "I think it (the climate) is different this time, and it's different because of what's happening at the moment.
"But when you knock on doors you have to expect to hear things you don't want to hear.
"People want to get things off their chest, but if you're given the time to explain things to them they will often give you the time of day, and I've had some good conversations."
Another candidate said: "I won't pretend I've not had people say things like, "You've got some cheek asking for my vote," but I haven't had anything I've not experienced before.
"Once you explain to people that this election isn't about Brexit, but about local services, people are often quite civil."
Local Democracy Reporting Service