The play, a musical called Darwin Rocks looks at the scientist's life and his theory of evolution.
A group of Christian parents said they would not allow their children to see the play as they felt one of the scenes mocked the views of the clergyman Samuel Wilberforce, a bishop who argued against
Darwin and his theory of evolution.
The play is aimed at 7- to 11-year-olds.
Hartford Manor Primary School, a non-religious community school in a village in Cheshire, decided to cancel the musical and replace it with a less divisive show following the objections.
That decision has provoked anger among another group of parents who argue that it is "unacceptable" that their children have been denied a valuable learning opportunity.
Alan McDonald, a parent at the school who wants the production to be brought back, told the Independant: "It really does feel like a huge step backwards.
"It doesn't seem even-handed or in any way right."
Other parents argued that there was a conflict of interest as the chair of governors at the non-faith community school is a local vicar.
Simon Kidwell, headteacher of Hartford Manor Primary School, said: "We thought it would be a problem to rewrite it. So we decided to change it.
"However, in hindsight I think that was a hasty decision. We could have put more effort into looking at whether we could have adapted it to make sure it was inclusive of everybody.
"I have apologised to the parents and we will consider putting it on in future years if we can make sure those bits are edited so it is inclusive for everybody."
The head added that the chair of governors had not played a part in the decision to cancel the play.
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