You cannot move or change stance while reloading your weapon or while switching weapons. This is an issue that majorly needs to be addressed as it effects your ability to fluidly operate within the game world. You should also be able to cancel player animations as a part of the context menu. While your are reloading there should be an option in the context menu that says "cancel reload" or "stop reloading" and you will stop, therefore enabling you to do something else with your character.