Controversial pundit has suggested it is nobody else's business if gaelic clubs are named after dead republican paramilitaries.
In the wake of Mr Robinson's address at a Co-operation Ireland dinner in Belfast last night, some unionists insisted the association still had much to do to improve relationships with their community, highlighting the specific issue of the naming of clubs and competitions after IRA and INLA members.
But former all-Ireland winner Mr Brolly, whose hometown club in Dungiven, Co Derry, is named after republican hunger striker Kevin Lynch, said the name issue was a "sideshow".
"It's nobody else's business - it's as simple as that," he said of the Dungiven club's name.
"People can either like it or lump it."
He said: "That's the way societies and communities work. Kevin played hurling for Dungiven and for Derry, and the hurling club was named for that reason. We're very proud of him."
Traditional Unionist Voice leader Jim Allister had been one of those who had raised the issue of club and trophy names following Mr Robinson's speech.
Mr Allister criticised Mr Brolly's stance.
"The remarks by Joe Brolly underscore just how foolish Peter Robinson was in attending last night's event and praising the GAA for supposedly reaching out across the divide," he said.
By David Young