Speaking in Birmingham, the senior Labour figure said: "On Tuesday a new Shelter report found 135,000 children will be without a home this Christmas.
"On the same day an analysis by the Equality Trust showed the UK's six richest people control as much wealth as the poorest 13 million. It all went to show just how unequal our society is.
"It's three weeks to Christmas. The celebration of the birth of Jesus.
"Children going hungry and homeless in the fifth largest economy in the world begs the question: are we really living up to the values of Christianity - or any other of our religions or beliefs for that matter?
"We don't believe it's enough to offer people a hand-up out of poverty. We want to abolish poverty.
"That's why we committed in our manifesto to abolishing in-work poverty within five years."
Mr McDonnell also accused the Conservatives of lying about the Hillsborough disaster.
He added: "This election campaign began for me in Liverpool, the city of my birth. Only last week, the people of that city were forced to relive again the trauma of the Hillsborough disaster.
"The memory of a previous Conservative government and how it treated the north, midlands, Wales and Scotland - football fans, and the working class.
"I remember the Hillsborough tragedy like it was yesterday. I remember the brave campaigners who have fought for justice ever since.
"I remember how my best friend, Jeremy Corbyn, one of the bravest of politicians, stood up for them, fighting for justice for those denied it.
"Those killed and then lied about at Hillsborough - including by the Prime Minister in his days as a journalist. People need to remember what the Conservatives have done to us over the decades."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.