Actually, in real life, the order of rotation does make a difference.
Reason, the 3 axis don't move, the object does, thus, it's relative x-, y-, z-coordinates change. That is, a book has a fixed width, length, and height, but, depending upon it's position, the width could be any of the three axis. Sitting on a desk, cover up, normal reading, the x-axis is page width, y-axis is page height, and z-axis is book thickness, where x- & y-axis are in the plane of the desk, and z-axis is sticking up into the air from the desk surface. To easily verify the rotation order, do full 90 deg rotations.
Rotate the book 90deg about each axis, in the order of z, then y, and then x. Result of each rotation:
none: as stated above
z-axis: book is still face up, but height is x-axis, width is y-axis, top of book is to the left.
y-axis: book is now standing, top is on the desk: thickness is x-axis, width is y-axis, and height is z-axis.
x-axis: book is now standing on the long edge, binding facing up: thickness is along x-axis, height is along y-axis, and width is along z-axis.
Now, return the book as before and reverse the order, this gives you:
x-axis: book is on top edge, binding to the left: x-axis is width, y-axis is thickness, and z-axis is page height
y-axis: book is on long edge, binding on the desk, top of book is to the right: x-axis is page height, y-axis is thickness, z-axis is page width
z-axis: book is on long edge, but in orientation that you would hold if you wanted to open the book to read normally: x-axis is thickness, y-axis is height, z-axis is width.
I gave the results to verify the direction of rotations and to spot any errors that I may have made. Keeping the rotations about the axis can be dis-orienting.
Ed.: Added drawing to help visio-lize.