Mark Sidebottom was presenting a report on the All-Ireland final on Wednesday night’s Newsline.
However, concerns have been raised by TUV deputy leader Ron McDowell.
He said the BBC would not have allowed one of its reporters to have their face painted orange when presenting coverage of the Twelfth.
But the BBC said it was “playfully intended in a report that was light-hearted in its content, tone and approach”.
Armagh face Galway at Croke Park on Sunday. The match will be broadcast live on the BBC and RTE.
But Mr McDowell, a Belfast City councillor, claimed many people had little interest in the match.
“The BBC are perfectly aware that the GAA is a contentious organisation which, by its association with republican terrorism by way of the naming of clubs, competitions and hosting of events, has repeatedly caused offence to innocent victims and division in Northern Ireland.
“It is inconceivable that a BBC reporter would have appeared on air with their face painted orange while reporting on the Twelfth celebrations.
“In fact, it’s scarcely believable that the BBC could carry a report on the Twelfth which wasn’t couched in negative terms because of the inherent bias of the organisation.
“Last night’s report was a clear breach of impartiality – which is hardly a surprise given the BBC’s record in recent months.
“However, there are many licence fee payers, including in Co Armagh, who want nothing to do with the GAA or the match on Sunday and for good reason. It’s high time our public service broadcaster realised that.
News Catch Up: Wednesday 24 July
“The BBC has lost the confidence of the public. Last night was another example of why the licence fee should be abolished.”
A BBC spokesperson said: “We had a live report from Davitt Park in Lurgan, reflecting local interest in/excitement about Armagh’s involvement in the upcoming GAA All-Ireland Final.
“We don’t think that the reporter’s decision to have the colours of both GAA teams on his face involved any breach of BBC impartiality.
“And it was playfully intended in a report that was light-hearted in its content, tone and approach.
“We know that Gaelic games are popular with, and important to, many BBC audiences – something that we seek to reflect within our output and as part of our reporting about all aspects of community and cultural life.”