Bremner revealed that he was called a "unionist lackey" and an "English toff" in the course of making a programme about Scottish politics.
Rory Goes to Holyrood, to be screened on BBC2 Scotland Thursday, is described by the comedian as "a mission to understand a bit more about Scottish politics and a desire to make a case for political comedy in Scotland" in the run-up to the referendum.
Bremner, who is from Edinburgh and lives in the Scottish Borders, said Scottish politics was "unlike any other area I've done before in that there is a great degree of hostility".
He continued: "I've not come across that before because it's taken as read – or has always been taken as read – that politicians are fair game for comedians. But that doesn't seem to apply across the board.
"The only agenda is a comic agenda. If people could just relax about this and about the fact politicians and politics are fair game for comedians, and that means politicians on both sides."
He recently called for the yes and no camps to "rein in their shock troops" after fellow comedian Susan Calman was subjected to threats and intimidation on social media following comments by her about independence on BBC Radio Four's News Quiz.
He said he believed the aggression in the referendum debate was due to the fact that it was about people's sense of identity which they felt "viscerally", particularly on the nationalist side.
"I can understand why there is a perception that if people make fun, they are somehow mocking the nation, but I think that's a misunderstanding."