Tree cutting and bird poop

I live in a busy urban area where trees have protection orders. The local independent school has asked for planning permission to significantly reduce the size of some Holm oak trees in their school grounds because the bird poop from the birds in these trees is damaging the play equipment in the play ground. There are obvious counter arguments like moving or cleaning the equipment. However there are some things I don’t understand about the impact on our local birds. Will cuttings the crown of a tree by 2/3 metres significantly impact the bird population? Are Holm oaks home to particular species of birds? Any advice gratefully received.