Hundreds of people have signed a petition urging two Co Tyrone grammar schools to suspend transfer tests.
They are demanding that schools use fairer criteria which does not penalise children hit hardest by the lockdown.
A dozen grammar schools have cancelled entrance tests this winter.
Parents are concerned that their children have missed too much school and will be ill-prepared.
St Patrick's Academy in Dungannon and St Joseph's in Donaghmore have said they will definitely use academic selection, however.
More than 100 past pupils of St Patrick's put their names to a letter in which they said entrance exams were not in keeping with the Christian ethos of the school.
It was signed by several notable public figures including civil rights leader and former MP Bernadette McAliskey and broadcaster and Irish News columnist Lynette Fay.
Now, Ms McAliskey and another past pupil Ann McGlone, the former CEO of the Willowbank organisation, have launched a petition.
They said children's access to education had been disrupted since schools shut in March.
"If children are able to return in September, it will be after an absence of five and a half months. Their return is likely to be in stages and some children may receive only 40 per cent of their learning in school depending on class sizes and available space," they said.
"In Mid Ulster, 12 per cent of homes are unable to access adequate broadband to support downloads or facilitate remote learning. Digital poverty means that children in working class homes are less likely to have independent access to a PC or laptop than children in middle class families.
"Children who are already socially or educationally disadvantaged are at risk of falling even further behind their peers, through no fault of their own."
They added that 11 Catholic grammar schools had committed to making alternative arrangements, recognising that "there has been disruption to the education of pupils since March 2020 and that there may be further disruption during the 2020/21 academic year".
"We urge the principals, trustees and governors of St Patrick's and St Joseph's to acknowledge the continuing impacts of Covid-19 and lockdown on all children, in particular those who are most vulnerable, disadvantaged and marginalised in our community.
"We believe this single act of courage and compassion on behalf of our local schools would provide immediate relief for children and their families as they look with hope to recovery, opportunity and equality."
