Are there reactions where the stirring direction would make a difference?
No, for three reasons:
Firstly, you need a relatively large molecule and/or a high viscosity and/or a strong shear/extensional flow, before the molecule even notices that it´s in a nonuniform environment. The molecule, if it has an elongated form, will then align perpendicular to the normal vector of that flow field. That only occurs for sufficiently concentrated solutions of polymers, or liquid crystals.
Secondly, you need three vectors to be able to differentiate a left and right hand. You only have the normal vector of the flow field, and the preferred direction of your molecule. Or in other words, your reaction will be indifferent to you watching it from the top of the beaker or through the bottom. ;)
Thirdly, to get a third vector into your system, you need the normal of the flow field to change significantly, in a specific direction (using, say, a propellor instead of a stirring bar), on the lenght scale of your molecules. That is impossible with a macroscopic stirrer.