Calls are being made for a review of parade routes after a priest was attacked as an Orange walk passed his church.
Parishioners of Canon Tom White spoke out after he was spat on twice outside St Alphonsus Church in Glasgow on Saturday afternoon.
Glasgow City Council condemned the attack and said officers would meet to discuss parade procedures on Thursday.
But the Grand Orange Lodge of Scotland said it opposed any restrictions.
A spokesman said restrictions would limit "freedom of expression" and that the lodge wanted to work with faith groups to target the minority who caused "trouble or offence".
The Archdiocese of Glasgow said that both Canon White and his parishioners were "subjected to vile abuse".
Police Scotland are investigating the incident as a hate crime. They have said that there was currently nothing to indicate involvement from a member of the parade, but that it remained one line of inquiry.
The parish pastoral councils of St Mary's and St Alphonsus', in the Calton area of Glasgow, have now raised concerns about three upcoming Orange walks which are scheduled to pass the churches later this month and in August.
In a statement, they said: "Despite a police presence, those involved in, and following the parade, were able to approach Canon Tom and the parishioners exiting the church. This happened against a backdrop of sectarian singing and sectarian insults.
"He was verbally assaulted and spat upon a number of times and members of the congregation, many who are frail and elderly, were subjected to the same treatment.
"While we welcome the statement by the Grand Orange Lodge of Scotland condemning the assaults on Canon Tom, as a community we are distressed and deeply saddened that in the 21st century we are unable to exercise human rights of freedom of association, freedom of assembly and the right to celebrate our faith in public: free from intimidation and violence."
Speaking to BBC Scotland Canon White urged politicians to take action to safeguard the welfare of his parishioners, and he revealed that he is due to marry two couples on the day the next procession is due to pass St Alphonsus.
He said the church and it congregation has had historic problems with sectarian abuse. On the morning he was attacked, he reported a number of abusive phone calls to the police.
"In many ways I've heard ad infinitum those in government say how modern and inclusive Scotland is," he said. "I think they might be blue in face before I believe it."
Parishioner Betty Corvi, church sacristan, said she witnessed the aftermath of the attack after hearing a disturbance outside the church.
"My priest is my next association to God, he's so important to me," she said. "And I had to watch him be degraded by all that.
"That's hurting me right to this day... You wouldn't do it to a dog so why would you do it to a man of God?"
Glasgow Cathcart MSP James Dornan said he would like to see agreement between the council, the police and the Orange Order to reroute future marches.
He told BBC Scotland: "I think it's been a flashpoint before, but obviously it's been taken to new levels at the weekend and it's unacceptable.
"What I would urge is that anyone taking part treats places of worship with respect, no matter what sort of places of worship they are."
A spokeswoman for Glasgow City Council urged anyone with information about the incident to contact the police.
She added: "A meeting with council officers will be held this week as it's perhaps time to review our procedures in light of a number of factors.
"We will also continue to liaise with Police Scotland, organisers, the Scottish government, third parties and stakeholders as part of the council's processions' code of conduct.
"Our aim is always to strike a reasonable balance between protecting the fundamental right of individuals and organisations to organise and participate in public processions, and the need to minimise disruption to the wider community by protecting the rights of all of Glasgow's citizens to go about their business without unnecessary disturbance and interference."
'Rights and freedoms'
However the Grand Orange Lodge of Scotland said it was against bans or restrictions on groups "simply because of their religious beliefs".
A spokesman added: "Limiting freedom of expression is a threat to a multi-faith society that we should resist at all costs.
"Instead, if we work together to target the minority in society that are out to cause trouble or offence, then that would allow us to work more closely with other faiths and groups to share a better understanding of each other's beliefs.
"From our own perspective, we are ready to work with others to gain this understanding. If Scotland is indeed a country of many faiths, many people, and many cultures, then we should be awarded the same rights and freedoms of others who choose to celebrate their own ideals."
Police are working to identify those involved in the attack and are trying to trace a man aged between 20 and 30 with a shaved head.