if religious matters didn't matter in the classroom then the state would not teach them as being false or ban them.
No teach in any public school is teaching that religion is false.
It bans creationism because it does matter.
It bans creationism because teaching creationism has no secular purpose and entangles the government in religious matters. Please google "Lemon Test" for more information.
The claim is that the church and state must not interfere with each other.
Yet the state is doing just that by teaching ideas contrary to the church.
No, it isn't. Teaching evolution has a clear secular purpose. Also, the government is not teaching that evolution or an old Earth are contrary to religious beliefs. Creationists are the ones teaching this.
you can't beat the logic here.
We can, and have.