The changes were made after fierce opposition from the Conservatives. Also dropped is the pledge to guarantee one-to-one tuition for 11-year-olds falling behind in literacy and numeracy.
The Bill is being pushed through before parliament is set to dissolve at the end of this week in the run-up to the election.
Children's Secretary Ed Balls blamed the last minute u-turn on the opposition party saying: "By sabotaging our Bill the Tories seem determined to deny children the extra help they need and to set back our drive to keep standards rising in every school.
"If Labour is elected children will get this support — and that's a guarantee."
But the Conservatives hailed the amendments as a victory for their party. A party spokesman said: "We supported having better sex education but the government insisted on removing parents' rights to withdraw their children from classes they thought damaging and we think parents must have such a right.
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