Reverend David Robertson, director of the Solas Centre for Public Christianity, described the development as a step backward and warned it could create a two-tier system with rural areas across Scotland being excluded from the pilot.
Royal Mail is opening delivery offices in parts of Glasgow, Edinburgh, Dundee and Inverness for four hours on Sunday as part of the trial programme, which will see more than 100 offices open across the UK.
Mr Robertson, minister of St Peter's Free Church in Dundee, said: "They say this is done for the convenience of customers but in our eyes it is a retrograde step."
He said extra opening hours would be a burden on workers, adding: "This is another erosion of the principle that one day in seven should be a day of rest. We deeply regret the move towards a 24/7 commercialised society where the only thing that matters is making money."
Royal Mail rejected the criticism, saying the change would benefit people who ordered items online.
Scottish spokeswoman Morag Turnbull said: "We are exploring ways to improve our flexibility and provide more options for people to receive items they have ordered online.
"People who will be staffing the offices on Sundays are doing so on a voluntary basis and the pilot sites are based on offices with the highest density of parcels."