I'd have nothing against a proper scientific experiment to see whether or not magic is real. But the scientific method absolutely requires falsifiability, so if you can't come up with a falsifiable hypothesis, then you're doing pseudoscience.
I notice you are using science and the scientific method interchangeably.
How can science study magic without knowing whether it is falsifiable first? Would that require them to do potentially unscientific/pseudoscientific things not becoming of a proper scientist? If we allowed that, next thing they'd be thinking without dogmatic constraints!
It's fine to do science without knowing up front whether something is falsifiable. One of the steps in the scientific method is to formulate a hypothesis. You can go up to that step even before you figure out whether you have something falsifiable; you just can't go past it until you do.
