Jacob Rees-Mogg accused Jo Coburn of singling out the views of the Roman Catholic Church during their discussion about the openly gay politician and leader of the Scottish Conservatives Ruth Davidson.
Asked whether he would support any decision by Davidson to marry her partner Jen Wilson, the MP for North East Somerset told the BBC Daily Politics said "the sacrament of marriage is available to a man and woman".
He added: "This is the teaching of the Catholic church, which I accept."
Earlier in the programme, Rees-Mogg described Davidson as a "formidably capable person" with "great political skills and wide electoral appeal" when asked whether he thought she had potential to lead the Conservative Party.
Coburn then suggested that Rees-Mogg's views on same-sex marriage could be perceived as "a problem for many people", given his position as a "senior politician."
Rees-Mogg posed the question: "I make no criticism of any of my colleagues but do you believe in religious tolerance?", to which Coburn replied: "I do."
The Tory politicians continued: "So, why do you pick on this view of the Catholic Church?
Coburn responded: "I am saying there are people who might have a problem with it."
Mr Rees-Mogg replied: "You are saying that tolerance only goes so far and you should not be tolerant of the teaching of the Catholic Church, so isn't this stretching into religious bigotry?
"The act of tolerance is to tolerate things you don't agree with not just ones you do agree with and the problem with liberal tolerance is it has got to the point of only tolerating what it likes.
Coburn, in turn, said: "Do not assume what I think or that I am attacking, I am raising an issue that your colleagues have also raised."
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