The front of the Belfast parade passed St Patrick’s Catholic Church in Donegall Street without incident.
No supporters of the Orange Order march were allowed along this part of the route.
A priest stood at the entrance to the chapel as the procession passed.
Some protesting residents stood nearby and also further up the road at Clifton Street, towards Carlisle Circus, where the parade beings.
The bands stopped playing music outside the church and went down to a drumbeat, resuming their music further down Donegall Street.
However, there was criticism that some parts of the Orange march made “multiple breaches of” the Parades Commission ban on music outside the church.
Sinn Fein MLA Carál Ní Chuilín said: “Several loyalist bands clearly flouted the Parades Commission’s ruling that bands should play only a single drumbeat close to and outside St Patrick’s Church in Donegall St.
“One band even started to play the infamous Famine Song as they passed the chapel.
“Ultimately the Orange Order is responsible for these breaches as it hires these bands. Time and time again the bands chose to stick two fingers up at the parishioners of St Patrick’s.
“The Orange Order claims it wants respect for its expression of culture but respect is a two-way street.”
Earlier, the parade was allowed to pass down the Crumlim Road, where Orangemen have been banned during their return walk later on Saturday.
Planned protests by nationalist residents groups were called off. Around 20 residents stood outside Ardoyne shops as the parade came past.
The residents told media that they were there to observe, not to protest. There was no incident.
The new PSNI chief constable George Hamilton had earlier visited the area to see the large security operation in the north of the city.
“I think we are in as good a place as we can be just now,” he said.