Alliance Justice Spokesperson Stewart Dickson said that the Orange Order was playing a dangerous game.
The Orange Order could no longer control the protest, he said, so they should go home.
But the Orange Order needs radically to rethink its role in Northern Ireland today.
Michael Phelan, from the Orange Order in England says he got a similar reception in Scotland.
The death of the Quinn boys was crucial to the weakening of the Orange Order's stubborn resolve.
The Orange Order has said it is involved in "quiet conversations" to address issues over parade disputes.
The Parades Commission has said it regretted that the Orange Order still would not meet for direct talks.
However, the Orange Order has a policy that it will not discuss disputed parades with local residents' groups.
However, the Garvaghy Road residents' group has been angered by the Orange Order's refusal to talk to them.
Jeffrey Donaldson joined the Orange Order at 16 and began his political career when he joined the Young Unionist movement.
But if the Orange Order is keen on replacing the Parades Commission, it will have to take the initiative itself.
Speeches condemning violence were made at two big marches, but the Orange Order leadership refused to condemn the fortnight's disorder.
The nationalist Bogside Residents Group objected to the Orange Order's application to the Orangemen's proposed parade route through the Diamond area.
This sounds like a challenge to the Orange Order, whose Grand Lodge policy remains not to engage in dialogue with Sinn Fein.
The Orange Order forbids members to marry Catholics or attend Catholic services.
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Tweed was also thrown out of the Orange Order after his conviction.
But the links between unionism and the Orange Order go very deep.
Meanwhile, the Minister for Agriculture, the SDLP's Brid Rodgers, has criticised the Orange Order for refusing to talk directly to the Parades Commission.
The Parades Commission has refused to review the decision despite appeals from the Orange Order and the North and West Belfast Parades Forum.
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It also emerged in recent weeks that the Orange Order convened secret unity talks between the DUP and UUP in early December.
The Orange Order has said comments by its Grand Chaplain over restrictions on parades "are indicative of a growing feeling of discontent among members".
Mr McGlone called on the Orange Order to condemn the threats.
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Mr Neale said that despite the Orange Order policy not to speak directly to residents' groups, Portadown District Lodge had "engaged over the past two years".
While the Orange Order's Belfast leadership officially opposes the Good Friday Agreement, many of those I spoke to at Rossnowlagh had voted in favour of it.
Last month the residents said they had lodged their objections with the Parades Commission because the Orange Order would not talk to them about the parade.
However, Mr Patton said at the 700th day rally that the Orange Order's official position of having no contact with the parades commission remained in place.
Republicans have been critical of the Orange Order and other Protestant marching groups for refusing to talk to Catholic residents in the areas where parades take place.
Police had warned they would make full use of anti-social behaviour fixed penalty tickets to tackle drinking in public, a move which was endorsed by the Orange Order.
Meanwhile, republicans have been blamed for a petrol bomb attack on a hall used jointly by the Orange Order and Church of Ireland at Aghalee in County Antrim.
The Orange Order said it "fully supports the sentiments expressed".
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