The Democratic Unionist Party has welcomed the plan to hold an Orange Order march in Dublin in May to mark the bi-centenary of the founding of the Grand Orange Lodge in Ireland.
Mr Paul Berry MLA, of the DUP, said the city's Lord Mayor, Ms Mary Freehill, should ignore Sinn Fein objections.
"There are quite a number of members who live in the Irish Republic who are members of the Orange institution and they must have the right to express their culture and celebrate their history in their own country.
"Sinn Fein/IRA once again are orchestrating protests to try and deny the rights and liberties of others to express their culture."
Mr Berry said Orangemen should "go out and have an enjoyable day". It will be the Order's first march in the city in over 60 years.
However, Mr Dave McSweeney, of the 32-County Sovereignty Movement, said the organisers and those taking part were clearly attempting "to undermine the besieged residents of the Garvaghy Road" in Portadown, Co Armagh.
"It makes a mockery of the suffering that these people have to live with on a daily basis. It would be more fitting if the Lord Mayor of Dublin stood shoulder to shoulder with the residents of the Garvaghy Road and witnessed the undisguised ugly face of sectarian bigotry first hand," he said.
Republican Sinn Fein president Mr Ruairi O Bradaigh said it would be "a denial of the plight of beleaguered nationalist communities, such as the Garvaghy Road and Lower Ormeau Road, to accept without protest an Orange parade".
Mr Tomas Mac Giolla, former president of the Worker's Party, said it was the democratic right of everyone to march.