Water softeners remove only "general hardness (GH)" ions like Ca2+, Mg2+, etc. and do not effect "carbonate hardness (KH)." For example, my tap water growing up, after hitting our home's water softener, was super low GH but fairly standard KH for the incoming city water. The general idea is that softeners exchange cation for cation, usually replacing the above "hard" cations with Na+ or K+. So carbonates (anions) shouldn't be impacted.
RO(/DI) systems remove pretty much all of the dissolved solids (TDS) which include the constituents of both GH and KH.
Regardless, the minor issues with using "softened" water are 1) you have no calcium or magnesium, which are still essential elements for plants/fish (although you could argue that feeding or target dosing could make that up) and 2) you're technically increasing TDS, which is what matters most to fish more so than pH/GH/KH. This is because the cation exchange resins swap one 2+ cation for two 1+ cations...thus you get a slight increase in TDS. It may not be much, but many people incorrectly assume that softeners are leaving you "purer" water.
I'd recommend bypassing the softener if you're using your tap water in any form. That's what was always recommended to me...luckily, I found that my kitchen faucet wasn't even connected.