Definitely don't use water from a water softener in your tank. You'd want to bypass the softener entirely.However my tap (with water softener)
Thrive? Potentially not. Survive? Sure. Some species will do better than others, of course, and some will thrive. You'll just need to find the right critters that work for your tank.Will neos (and ultimately most fish) be able to thrive in these parameters?
I don't see gH being an issue for many common species and certainly not Neocaridina shrimp. But the high kH could be a real issue with some species and could make it tough to grow some plants.
You could consider using something like peat to soften your tap water or a higher end active/buffering substrate like ADA Aqua Soil Amazonia. Both routes would lower kH a bit. But... to make things easier... have you thought about keeping harder water species instead of common community fish in the hobby? There are some Cichlid varieties that would make for a killer tank, for example. There are also Guppies, Mollies, some Tetras and others that may be good options. I've even seen some Killifish that do well in really hard water.
You said you don't want to dilute your tap water but if you're only changing 10% of your water every week or so, it may not be too complicated. Especially if you go 2 parts tap to 1 part RODI or 3 parts tap, 1 part RODI. That would mean you have to buy RO water significantly less often than you would if you were going 50/50.
Stability is key and once you get your critters acclimated, I think you'll be able to do well with those parameters. Just have to find what works for you.