THE RUC decision set a dangerous precedent, Alliance Party deputy leader Mr Seamus Close has said.
"It is now going to be very difficult for anyone, including the government, to argue that might doesn't equal right in Northern Ireland.
"The reversal by the RUC of their original decision gives the strong impression that mass civil disorder and mob violence can dictate the operational decisions of the police. This is a black day for Northern Ireland and for law and order", Mr Close said.
Those who brought protesters on to the streets must bear responsibility for the violence and anarchy that ensued, he added.
"The Orange Order have achieved a Pyrrhic victory. Are unionist leaders happy to have achieved this result after the mass violence and thuggery that has been carried out in their name?"
The Iona Jesuit Community in Portadown, in a statement, also expressed dismay and said the RUC decision was a victory for might over right. "It undermines yet again the prospects of building a new society in Northern Ireland based on mutual respect", it said.
Mr Ruairi O Bradaigh, president of Republican Sinn Fein said the British government had collapsed in the face of loyalist force and bullying. The clergymen had been blatantly used as a decoy as the RUC was positioned to force through the Orange march.
DUP Councillor Sammy Wilson said the reversal of the Chief Constable's decision would be greeted with relief across the North but was not an occasion to "fly the flag of triumph". The outcome was a good result for common sense and civil freedom he said.
The SDLP Belfast Council Group met in emergency session last night to discuss the security and political situation.
The Communist Party of Ireland strongly condemned the actions of the RUC and the Orange Order.
The RUC violence was uncalled for and only reinforced the call for its disbandment, a statement said.
The party also called on the Government to have an inquiry on yesterday's events. The actions of the RUC and the Orange Order could only lead to further tension and violence across the North, the statement said.
The CPI appealed to the nationalist population to remain calm.