conductance will vary based on both impurities and dissolved gases.
If you are diluting acid for initial fill then I would be more picky.
I would use 5uS as a limit if someone wanted a number. This water can be either distilled or deionized.
If you live where you have soft water naturally (not through a softener) it would work fine for top off.
5 ppm as chloride is the usual limit for lead acid batteries - believe that translates into less than 2 microS/cm conductivity. good distilled water is less than 0.1 microS/cm
if you want your batteries to last as in station batteries, tap water is not a good idea unless you have a treated water RO system in place. Tap water is okay for consumer use, but it does shorten battery life
Depends on what type of water is being distilled. Seawater stills to typically have some small amount of salt carryover. That is why they have salinity cells on the distillage lines which dump the distillate if the carryover gets too high.