Lord Singh of Wimbledon will no longer deliver Thought for the Day on BBC Radio 4.
Known by listeners as Indarjit Singh, the journalist has been accused the corporation of "prejudice and intolerance", according to The Times.
His comments came after the BBC tried to stop Lord Singh from broadcasting an item commemorating an executed Sikh guru "because it might offend Muslims".
The Sikh guru cited had opposed the forced conversion of Hindus to Islam under the Mughal emperors of India in the 17th century.
However, the script, which was broadcast in November last year, had contained no criticism of Islam.
Lord Singh told The Times: "It was like saying to a Christian that he or she should not talk about Easter for fear of giving offence to the Jews."
The BBC is understood to have allowed Lord Singh to read the script only after he threatened to leave the Radio 4 slot rather than have his religion's teachings "insulted in this way".
The 87-year-old crossbench peer subsequently filed a complaint about the way he had been treated, claiming it was not the first time he had been prevented by the BBC from addressing subjects important to the Sikh faith.
The complaint was ultimate rejected after BBC director of radio James Purnell ordered a review.
Thought for the Day has been part of Radio 4's Today programme since 1970.
The decision by Lord Singh to quit follows a row over comments made by BBC breakfast host Naga Munchetty about US president Donald Trump that prompted the corporation to initially partially uphold a complaint against its own presenter.
Lord Singh said: "The need for sensitivity in talking about religious. political or social issues has now been taken to absurd proportions with telephone insistence on trival textual changes right up to going into the studio, making it difficult to say anything worthwhile.
"The aim of Thought for the Day has changed from giving an ethical input to social and political issues to the recital of religious platitudes and the avoidance of controversy with success measured by the absence of complaints.
"I believe Guru Nanak [the founder of Sikhism] and Jesus Christ, who boldy raised social concerns while stressing tolerance and respect, would not be allowed near Thought for the Day today."
A celebrated interfaith activist, Lord Singh went on to accuse the BBC of "a misplaced sense of political correctness".
He claimed in 2011 he had told told to scrap plans to talk about the birthday of Guru Nanak and instead discuss the "forthcoming marriage of Prince William with Kate".
"I reluctantly agreed to do so, to the upset of many Sikh listeners," he said.
BBC director general Lord Hall of Birkenhead said in a statement he had every confidence in the slot and that Lord Singh might seek a solution using "the BBC's complaints process".