Delivering his farewell sermon before his retirement as Bishop of Durham next month, Bishop Wright challenged the notion that being interested in social justice meant denying the resurrection of Jesus, whilst being interested in eternal salvation meant having to treat the world as irrelevant.
He urged Christians to speak out in the face of injustice and give hope to those in difficulty, such as the poor and asylum seekers.
He said: "Some voices are suggesting we should now put the cart before the horse and have the church dance to whichever tunes the government of the day want to play. Not so.
"That is simply to allow the iron law of political correctness to trump the liberating grace of Jesus.
"The church must not only work for justice but must challenge the world's self-serving notions of what justice is and how you get to it.
"We must do it in relation to genuine compassion and caring for people who get squeezed out, not because we're following political fashion but because we are to be people of hope – not only people who hope, but people who are the cause of hope in others."
Bishop Wright retires on August 31 to take up a new academic position as Research Professor of New Testament and Early Christianity at the University of St Andrews in Scotland.
Durham Cathedral was packed for the service of celebration and farewell, which was joined by local church leaders, including the Roman Catholic Bishop of Hexham and Newcastle, the Rt Rev Seamus Cunningham.
Bishop Wright paid tribute to the positive change in ecumenical climate among local church leaders in the last few decades. He said Christians needed to learn "how not to please ourselves" but make room for one another and live in harmony.
He said: "It is fatally easy to squeeze out or sneer at people who for whatever reason appear not to fit our model; and when we do that, we more or less guarantee that they will not be able to hear, let alone believe, the message about Jesus that we preach."
He continued: "It's fatally easy to imagine that all my prejudices are theological convictions and that all your theological convictions are mere prejudices.
"That's not to say that there aren't such things as genuine convictions and prejudices, only that it's often difficult to sort out which is which."
He admitted that welcoming others was not easy and that Christians still needed to be able to tell the difference between the "differences that make a difference and the differences that don't make a different".
"Paul writes enthusiastically about overcoming the barriers put up by our ethnic backgrounds, but he also writes elsewhere about destructive patterns of behaviour which destroy Christian fellowship and which cannot be treated as differences of opinion to be overcome by a fuzzy 'inclusivity'," he said.
Bishop Wright acknowledged that the diocese had faced hardship in recent years with cuts in clergy numbers but paid special thanks to parish clergy having to look after two, three or even up to seven parishes simultaneously because of shortages.
He appealed to them to be a people of hope rooted in Jesus and not "collapse into mere optimism or a grinning denial of reality".
Other guests at the farewell service included the Vice Chancellor of Durham University, Professor Chris Higgins, and the Mayor of Durham, Councillor Mamie Simmons.