When we used bias-belt tires, we used to cross them. They were not very sensitive to changes in direction of rotation.
When we moved to radial tires, I stopped seeing anyone crossing tires. The thinking was that radials develop a physical familiarity with the direction of rotation, even if they are not the high-end tires that are built to only be used in one direction.
Perhaps it is for this reason, everywhere I went I saw only examples of front-to-back rotation of tires.