Politicians and community leaders said the Glasgow Orange Defenders, which faces potential police action, had been deliberately provocative and "exploited their freedom" to return to Scotland by playing outside St Patrick's RC Church on Donegall Street during a mass.
It comes amid wider concerns over the behaviour of some bands making the trip from Scotland to Northern Ireland's main Loyalist parades.
One eyewitness said that much of the aggravation between bands and protesters at a well-known parade flashpoint was coming from Scots bands.
Glasgow Orange Defenders, based in Yoker, breached a ruling by the Parades Commission on playing music outside the church 10 days ago.
The Parades Commission is responsible for placing restrictions on marches in Northern Ireland it deems contentious or offensive.
It acted after a Belfast-based band sparked controversy in 2012 playing the Famine Song outside St Patrick's. That band was subsequently prevented from parading past the church.
Alban Maginness, a prominent member of the moderate Nationalist SDLP and local member for the Northern Ireland Assembly, called for sanctions against the band.
He said: "It would, in my view, be appropriate to ban them from any further participation in parades in the area or indeed in Northern Ireland at large.
"There are huge historic sensitivities around St Patrick's and this band is in a situation where they can carry on and no-one takes much notice of them back in Scotland.
"They've a freedom they wouldn't have in Scotland and they've exploited that freedom to make a statement. But it would be a wrong assumption to make that if you're back in Scotland you're virtually untouchable."
During the morning march members said they performed Land of Hope and Glory, before playing Abide with Me on the return parade at around 7pm.
According to reports, as the band approached the church its members appeared to be having an argument about whether or not to play. An Orangeman marching behind the band reportedly came forward and remonstrated with the band.
After the incident, Stuart Leckenby, band sergeant with the Yoker-based outfit, issued a statement on Facebook. He said: "If playing a hymn passed [sic] a Christian place of worship is wrong then we must be guilty. If asked if I would change or play anything different? Never. We are what we are."
Spokesman for the local residents' group Frank Dempsey said Glasgow Orange Defenders and other Scottish bands found to have breached Parades Commission determinations should not be allowed to return to the north.
He said: "That band should be banned from coming here. Why should they be allowed to come from Scotland to do their deed outside the church and then go back? The Scottish bands should be seriously looked at."
A spokesman for the Police Service of Northern Ireland said: "An evidence-gathering operation is in place and any breaches of the Parades Commission determination will be investigated and reported accordingly."
The Parades Commission said evidence provided to it was confidential but a spokesman added: "The Commission will, however, take any proven breaches into account in reaching future decisions on a public procession."