Media regulator Ofcom has received 1,500 complaints after the highly sexual nature of the performances by Rihanna and Christina Aguilera during the show, which was broadcast before the watershed. ITV is believed to have received a similar number of complaints.
Although Rihanna's skimpily clad performance of "What's My Name" has caused concern among viewers, the outrage appears to be directed mostly at Aguilera's performance of her new song "Express", from the soundtrack of big screen musical "Burlesque", in which she stars.
She appeared on stage with backing dancers wearing nothing but bras, knickers and suspenders. Their provocative dance routine at times simulated sex and has been likened by critics to pornography.
Simon Calvert, of the Christian Institute, said ITV had made a "catastrophically bad error of judgement" in allowing the production to go out before the watershed.
He expressed concern over the effect of such performances on young people in particular.
"Lots of people are concerned and parents are particularly concerned about the effect this kind of thing has on their sons and daughters," he said.
"Daughters are made to feel that this is a normal way to behave in public and sons are taught to expect women to behave like that. It is very unhealthy."
Mr Calvert said the level of concern expressed over the performances ought to both encourage and challenge to Christians.
"It shows we are not the only ones to be concerned about the plummeting standards of decency in broadcasting," he said.
"Christians have something unique to contribute to the discussion. As Bible believing Christians, we believe in values like dignity and virtues like modesty and we ought to be more courageous in advancing these values and virtues, whether it's with the neighbour over the garden fence or from our pulpit."
The X Factor final pulled in around 20 million viewers on Saturday night. Many of them would have been children.
According to the Daily Mail, Equality Minister Lynne Featherstone added her voice to the chorus of criticism.
She said the performances should have been "less raunchy" because of the children who watch the show.
Ofcom said it would look into the complaints before making any decision over whether to launch a full inquiry into the show.
According to its broadcasting code, the portrayal of sexual behaviour must be "editorially justified" if it is shown prior to the watershed.
Pippa Smith, of Safer Media, hit out at ITV's decision to allow the performances on a programme aimed primarily at families.
She said it was "extraordinary" the acts had been allowed to air in the same week as the Government had launched a major inquiry into the sexualisation of children in Britain.
She said: "I can't see what editorial justification there could be."