Some groups felt that Hoddle should not have been sacked for expressing private beliefs, but the overwhelming view was that he was right to step down.
The Sports Minister, Tony Banks, said: "It is a personal tragedy Glenn Hoddle's career as England coach has ended in this fashion.
"He is a decent man but his views as expressed ... caused distress to many disabled sportsmen and women who have achieved so many sporting triumphs for the country. It is now for the FA to move swiftly to find a successor in order that England can qualify for the 2000 European Championship finals."
David Mellor, chairman of the Football Task Force, said: "I take no pleasure in the demise of Glenn Hoddle but I do not think he gave the FA any choice.
"His personal beliefs have become inextricably linked with his job. English football was being dragged down by Glenn Hoddle's bizarre beliefs."
He congratulated the FA for its handling of the situation and said Hoddle's replacement faces a "really tough assignment".
Mencap, the largest disability charity, said it "wholeheartedly" supported the FA's decision and branded Hoddle's comments as "dreadful".
Sarah Talbot-Williams, Mencap's head of communications, said: "Glenn Hoddle's exit is a victory for fair play in football and among people with learning disabilities.
"It is only right that the English coach pays a just penalty for comments which caused great offence and fuelled more bigotry to those who already face prejudice."
Peter Ainsworth, the Tory spokesman for culture, media and sport, said: "I entirely respect the decision of the FA, who have, no doubt, come to their conclusion on the basis of what they believe to be right for the sport."
Mark Oaten, the Liberal Democrats' disabilities spokesman, said: "It is always sad when a career ends in this way, but the decision by the FA on Glenn Hoddle is the right one. It will restore confidence in the national sport and it will begin to build bridges with disabled people.
"The one positive thing to come from this whole sorry affair is the widespread support from the public, politicians and the media for the disabled."
Hoddle's former wife, Anne, broke her silence following their divorce last month. "Obviously we are all very sad for Glenn, especially as he's got to face it all in the glare of publicity," she said. "But it is a sad day for British tolerance and freedom of speech."
Peter Stothard, editor of The Times, said that he took no great satisfaction at Hoddle's dismissal. "It was the right decision. He had made his position untenable. A man in his position cannot go around offending people," Mr Stothard said.
Monica Hartland, deputy chairman of the National Federation of Football Supporters' Clubs, said: "Glenn dug himself a hole and, although it appears that he jumped into it, he was, of course, pushed, and with considerable force.
"The eccentric Hoddle departed because it was put to him, one suspects, that he had 'lost it' with the players."
A spokesman for the Nationwide, England's team sponsor, said:"We are pleased that the FA has acted decisively.
"Our position as the sponsor of the England team has been to ensure that we were not associated with views we thought would cause distress to our members."
But the Labour peer Lord Ashley, who was totally deaf for some 25 years, said: "An aggressive media, a weak Football Association and his own lack of judgement have finished Glenn Hoddle. He should only be sacked if he is a failure as England's football coach, not because of his religious opinions."
And Wayne Busbridge, who is blind and advises the Football Task Force on disability issues, said that the FA was wrong to sack Hoddle over personal beliefs. "It's a bigoted view but I am strong enough to carry on with my work without letting it affect me," he said.
"At the end of the day he should be judged on his results and not on his views, although it was unwise to express them so publicly."
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