Mean geometric chord of exposed wing, or mean aerodynamic chord of gross wing? It's not particularly clear in the literature.
Reynolds number is a variable parameter. There are multiple definition and you can use one of the two MAC, the important thing is that you specify the reference of your calculation. Usually between MAC of gross and exposed wing it would not change a lot(I would expect 10% changes), and seen that we are speaking of the order of magnitude of at least 1*10^6 for a commercial aircraft wing, the changes are negligible. Moreover, Reynolds number must be read with respect to the particular phenomenon you are using it for. For example as a reference value for a transition computation from laminar to turbulent on the wing, I would use MAC of the exposed wing, it would seem to me more appropriate seen that the gross one have a strong interaction with the fuselage.
Depends on what you are trying to accomplish. If you are comparing different aircraft, it probably doesn't matter as long as you always do it the same way. If you are designing a wing, the exposed area is what matters. If your wing has taper, you might want to determine the number at multiple points as the tip will be lower than the root, and might be able to use a different airfoil.