Lefty here. I agree with Earlene. The only type of cutter that is harder for a lefty to use is a blade with a bevel on only one side, such as a serrated knife.
If your cutter does not have any bevel (such as a bench scraper or wire cutter) or if it has a bevel on both sides of the blade (such as a regular knife), a lefty has exactly the same chance as a righty of making a clean cut. If you're using these types of cutters and getting poor results, I'm afraid your handedness isn't the reason.
A big reason why you cannot make parallel, even cuts is the cutter you're using isn't designed to be accurate enough for the job.
Most "miter box" type cutters (first photo) have slots that are too wide so the cutter doesn't slice down consistently. If there are multiple slots (as shown in the first photo), the slots may not be perfectly spaced. Even 0.5 mm variation will make a distinct difference in the weights of the bars. Also the blades used for these cutters can deflect and bend slightly, especially if your soap is firm, giving a wavy or slanted cut.
Most cheese cutters I've seen simply aren't designed to cut accurate slices. The wire isn't tight enough, the hinge is sloppy and rather weak, and there is no fence nor "stop" to guide the soap properly. A soap wire cutter (Joyful's photo) is far better.
Bear in mind the thickness of the soap will also affect the final weight, even if you try to get the top of the loaf perfectly flat. So even if you are able to cut perfectly parallel, even slices of soap, there will always be some variation in weight.