Speaking ahead of a red carpet screening of Braveheart at the Edinburgh International Film Festival, the Hannibal Lecter star called for activists on both sides of the debate to show “dignity and respect” to their opponents.
Cox’s intervention came after the Harry Potter author was abused online after expressing support for the Better Together campaign, which she has donated £1 million towards.
Cox also defended Braveheart, the Oscar-winning epic inspired by William Wallace’s heroics, against claims of anti-Englishness and also insisted Mel Gibson’s famous film had “nothing” to do with Scottish nationalism.
He was speaking hours after legendary Scottish comedian Stanley Baxter attacked Braveheart for stoking anti-English sentiment in Scotland when it was released 18 years ago.
Cox said: “You have to consider and respect people’s opinions, just in the same way as people to have to respect people like JK Rowling.
“They are perfectly valid and she has her reasons for doing it, good luck to her.
“I disagree with her, but she has every right to say what she thinks. That is what a democracy is about.
“I don’t like anybody being abused - from both sides. There is no need for it.
“You have to behave with dignity, with propriety and respect, especially on a subject like this which is a major thing in our lives.
“You really have to be respectful. There is no need for it. She has done a lot, that women. She doesn’t deserve it.”
Meanwhile Cox, who was sporting a “Yes” badge on the tartan carpet outside the screening at the Dominion cinema, said it would “hysterical” for anyone to suggest Braveheart was an anti-English film.
Baxter had earlier entered the independence debate, by criticising “dreadful” films like Braveheart for a rise in support for independence.
He told The Scotsman: “Braveheart is nothing to do with Scottish nationalism, that’s the one thing it’s not about, it’s about Scottish independence. They are two entirely different things.
“The trouble with anything as contentious as Braveheart, especially when the enemy is the auld enemy, is that it’s always going to look anti-English.
“It’s not anti-English, of course it’s not. It’s a story, it’s a drama, it’s something that we went through when there was a bit of a row going on, a big row at that.
“I don’t really buy this anti-English thing - I think that’s a bit hysterical, quite frankly. And also, it’s a movie, for god’s sake.”
Meanwhile Cox’s co-star Peter Mullan, who was also wearing a “Yes” badge, said the likes of Rowling and Baxter should be able to voice an opinion without being subjected to abuse.
But he said he was convinced “underhand” tactics and “dark arts” were being deployed to stoke up ill-feeling.
The award-winning actor and director said: “The beauty of what is going on is that everyone is quite rightly voicing their opinions.
“I genuinely and strongly believe people should be allowed to voice an opinion and not get abusive texts or emails. It is beyond disgusting and is not the kind of Scotland I want to see.
“I do think there is some underhand stuff going on with regards to the nastier side of things.
“Further down the line I would like to know who was really behind it. I think there are some dark arts going on - bit that’s not to say there are not nutcases out there writing this sort of ****.”
Meanwhile Gibson sent a surprise personal message to the film festival event, recalling how the cast and crew of Braveheart had “went into battle” to get the film made. Speaking in a message recorded in New Mexico, where Gibson is making his latest film, Blood Father, he said: “It is hard to believe that we actually went into production on the film 20 years ago this month.
“We had a load of hopes and dreams about what it could be and what it might be.
“We weren’t disappointed. I was very proud of it and I was also very proud of all the other people who assisted me in achieving our goal.
“There were a lot of talented people - cinematographers, set designers, actors - and together we went into battle with the goal of telling a great and compelling story.
“The fact we’re commemorating this 20 years later is testament that we probably achieved our goal, which makes me very happy and proud.”