How to determine if the amount of manganese chloride will change neural resting potential
For theoretical calculations with other ions, you need to know the concentration and permeability of each of the major ions inside and outside the cell, both with and without the added substance (in your case MnCl2), and then use the Goldman equation/GHK equation to calculate resting potential before and after. Approximations would probably be sufficient.

However, chloride can be a bit complicated because the intracellular chloride concentration can fluctuate with extracellular chloride moreso than the other major ions. Therefore, depending on the sensitivity of your experiment, you may need to perform whole-cell patch clamp recordings to measure the resting potential directly.

If the change in chloride is a small percentage of the total, you can probably consider the influence to be negligible.