Parents at Oak School in Huddersfield claim the crest worn by pupils was changed to avoid offending those of other faiths.
Ciarán Kelly, from The Christian Institute told Premier's News Hour he isn't convinced someone would be offended by the faith symbol.
He said: "We need to get away from this idea that somehow to put up a cross or to manifest the Christian faith in the public sphere is somehow unacceptable.
"Church of England school - if you want to have a cross on your logo, have one."
He went on: "I don't think anybody is going to be shocked and surprised by the idea that a Church of England school is going to have a cross as part of its school badge and its logo."
Oak C of E School released a statement via Kirklees Council.
Head teacher David Bendall said: "The logo featuring a cross was a temporary design whilst we made the transition to becoming Oak Primary School.
"It was not confirmed as the final logo and was amended to give more prominence to the tree, which not only reflects the school name but is also an ancient symbol representing many beliefs.
"Changing the design to include three branches also meant we could signify the way Oak Primary was formed, which was three schools joining together as one.
"The decision was made jointly by governors and the diocese and the change does not in any way alter the identity or ethos of our school.
"We are a very diverse community school and it's central to our ethos that children of all backgrounds are treated exactly the same.
"We hope people will agree that a logo is only a symbol - a school's qualities are not brought alive by a picture but by the thoughts and actions of the people within it."
The diocese also released a statement that reads: "The school had said it was largely a question of choosing a simpler design, and the three branches of the tree represent the three schools that have come together (one of which is CofE).
"Many CofE schools don't have a cross in their logo.
"The school is not remotely apologetic about its Christian roots, its Christian values are expressed through the atmosphere and ethos of the school."
Listen to Premier's Marcus Jones speak to Ciarán Kelly here:
