Dalit scholar Kancha Ilaiah said Prof Nandy had made "a bad statement with good intentions".
Shadow minister for children, Labour's Lisa Nandy, said Mr Loughton had raised a "serious issue".
Sociologist Ashis Nandy was reported as saying that some of India's most disadvantaged groups were the "most corrupt".
Poet Ashok Vajpayee said Prof Nandy was a "serious thinker" and had made the comments in a certain context.
BBC: Ashis Nandy: India police probe academic for 'caste slur'
The police said that Prof Nandy had been summoned for questioning and the festival organisers told not to leave Jaipur.
Very few people seemed to be listening to Prof Nandy's patient clarifications.
Professor Ashis Nandy, a sociologist and commentator, was reported as saying that some of India's most disadvantaged groups were the "most corrupt".
BBC: Ashis Nandy: India police probe academic for 'caste slur'
Leading academic Ashis Nandy is threatened with arrest after he makes controversial remarks about corruption and disadvantaged groups at the popular Jaipur literary festival.
But the court advised Mr Nandy to be more cautious when speaking.
India's Supreme Court has ordered the police not to arrest leading academic Ashis Nandy for making controversial remarks at the Jaipur Literature Festival.
The split is evident in Labour's frontbench education team, which is led by the Blairite Stephen Twigg but also contains the more sceptical Lisa Nandy.
The organisers have also handed over to the police a video and a transcript of Prof Nandy's remarks during a panel discussion at the festival on Saturday.
All hell broke loose: there was a tsunami of media-generated outrage, a police complaint was lodged against Prof Nandy, and prominent Dalit leader Mayawati said he should be sent to prison.
The outsize controversy over the remarks made by Prof Nandy, who was once voted one of the world's top 100 public intellectuals by Foreign Policy magazine, demonstrates how fringe groups can threaten free speech with impunity.
On Friday, the bench headed by Chief Justice Altamas Kabir told Mr Nandy that he must "exercise caution" in the future if the "intention was not to cause hurt to the sentiments of another person or community".
Prof Nandy later clarified his comments.
BBC: Ashis Nandy: India police probe academic for 'caste slur'
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