I believe hard vs soft water is really the wrong discussion to have, as it relates to leopard gecko health.
Water that is considered hard contains higher levels of calcium and magnesium salts than that which is considered soft. It should be noted that that these salts are minerals which we strive to keep in the diets of our pets. I don't use any softening techniques for my pets, I'll explain why a bit later.
There are actually two kinds of hardness, carbonate hardness and permanent hardness. Carbonate hardness is the result of calcium bicarbonate and magnesium bicarbonate salts dissolved in the water. These salts are easily broken down by boiling, resulting in a reduction of the overall hardness of the water. Permanent hardness is the result of sulphate and chloride salts, and these can only be removed by more aggressive softening techniques, such as ion exchange, distillation, or RO/DI (Reverse Osmosis/De-Ionization).
All three of these softening techniques have their risks, and it's important to understand them before considering whether or not to employ them. Ion exchange is performed by passing water through a resinous material rich in sodium and/or potassium to replace the calcium and magnesium ions. The most commonly available ion exchange systems are "softener pillows" which are porous bags of resinous granules designed to either pour water through, or soak in a container of water to be softened. The net effect this has on our pets is alarming. It basically removes biologically desirable chemicals and replaces them with chemicals which are intended to decrease those vital minerals inside their bodies. In other words, using ion exchange softened water is likely removing calcium and magnesium from our leo's bodies. I don't know if this effect is sufficient enough to actually cause MBD, but I'm certainly not going to find that one out the hard way!
Distilled water, and RO/DI water both have largely the same risks. They are so purified that when they are ingested, they may leach nutrients from the tissues they pass through. In other words, the absence of any dissolved compounds in solution creates an imbalance when it passes through the body of any organism which is resolved by robbing dissolved minerals from the body tissue. This can lead to degradation of intestinal walls to the point of causing diarrhea. The same goes for humans, if we drink this ultra-pure water, it will sicken us quickly.
The first part of the RO/DI process, stand alone Reverse Osmosis, is becoming more common and less costly. It's also less aggressive, and probably less detrimental than the other methods.
My personal preference is to not use any water softening methods. The tap water where I live is quite hard, and has been chlorinated at the treatment plant. I use ReptiSafe water conditioner drops to remove any chlorine before pouring tap water into the water bowls, and I wash the water bowls once a week with Dawn dish soap. There is no scale building up in the water dishes, but even if there were it's not a problem for our pets. The only other water use for my pets is in spraying the moist hides. I have store bought spring water on hand which I use to spray many of the plants I keep in my herp room, and use this same water for the moist hides.
I hope this helps!
Todd