Speaking in the House of Lords, the Most Rev Justin Welby highlighted "a notable absence of genuine dialogue" and stressed the need to be able to "disagree well".
Highlighting the benefits of diversity, the leader of the Church of England argued that monopoly views, be they secular or sacred, allowed people "to live in bubbles of mutual incomprehension and even ignorance".
He made his remarks during a debate in the upper chamber on the challenges posed by religious intolerance and prejudice in the UK.
It came in the wake of the publication of figures that showed a sharp rise in hate crime last year.
Data from the Home Office revealed the biggest hike was in religious hate crime, which rose by 40 per cent from 5,949 in 2016/17.
Referring to the "rising tide" of anti-Semitism and Islamophobia, the Archbishop said: "This terrible storm-ridden climate is affecting people across a whole range of religious traditions."
He said: "It's clear that debate in Britain across a range of issues risks losing the gains we have made in the post-war period, gains of civility and respect.
"There is a notable absence of genuine dialogue and listening to different views."
He told peers there were "many Christians with whom I disagree on the expression of their views in particular areas".
"However, even where I disagree, I want to uphold the right of these people to say things that are neither fashionable nor conventional today."
Highlighting the recent "gay cake" case where the Christian owners of a bakery won a Supreme Court appeal over a claim that they had discriminated against a customer, Mr Welby said: "Although there might be things in that case that I would question, it is a thoughtful, erudite and profound examination of the intertwining of freedom of belief and freedom of expression."
He added: "We must seek a society that is able to voice disagreement freely and to disagree well.
"Monopoly views, secular or religious, merely enable people to live in bubbles of mutual incomprehension and even ignorance."
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