Kh and Gh
Gh refers to the overall hardness and includes metal ions like iron oxide and copper (usually from pipes).
Generally the iron isn't something to worry about and if your house has copper pipes let about 4 gallons of water run first and that'll solve that.
In specifics Iron is not the right hardness for aquarium water. If I were to have a Gh of 9 and a Kh of 2, I'd want to increase my Kh using products that add carbonate to the water. In order to do this I need to be very aware of my pH. Adding straight baking soda (bicarbonate soda) will drive the pH up over 9.4. Many products for controlling pH exist, they contain a combination of carbonate and phosphate. These are used ONLY in freshwater as the high phosphate is baaad for saltwater/marine.
Carbonate ballasts pH up, phosphate ballasts pH down. You can create a sort of electrochemical balance in the water using both which will guide the pH to whatever level you like and some products, like Seachem's, are very effective at what they do.
If you use softened water it would be a good idea to wait until the brine solution runs a regeneration on the ion resin then take a sample of the new fresh water to your LFS to test for general and carbonate hardness as well as pH of the water. Don't dechlorinate it, take it as it comes from the tap.
The tricky part about hardness is that it is bound to alkalinity. Whole different conversation but sufficient to say if your hardness aproaches zero your tank pH starts to swing around based on other chemistry such as feeding time and photosynthesis. The alkalinity will be light so the "power" of the pH variations will be weak but they'll still swing around AND tend to be below 6.5.
I commonly use an ion resin bag in a filter in my top-off water process and I usually use it when I make replacement water. The difference is that when I make replacement water I only use it for about 10 minutes per 2.5gal (submersible canister filter). When I make top-off water I will run it for up to two hours. This ion resin bag IS what is used in water softeners. Keep in mind that while the softener DOES reduce hardness in the water it also puts sodium into the water in its place. Drinking softened water occasionally is ok but even at its worst the iron heavy water is better for you.
As water evaporates from the aquarium it does NOT take the hardness with it. If you have fairly hard water and top off with more you will slowly drive the hardness in the tank up. A good measure of too much hardness is when the air stones stop making rolling bubbles.
I doubt your water softener gets close to the 2.5Gh/2Kh I reach in my make bucket after two hours run. These numbers are drops of test which translate to just under 18ppm per drop. So we're talking 44ppm/36ppm.
This above is all to bracket something very important. If you have a tank you are trying to establish cycle in or have a tank you intend to keep a lot of plants and fish in you need to keep your carbonate hardness (Kh) up around 150ppm or higher but not higher than 230ppm. Hardness, Nitrate and salt compete for space between the water molecules and having all three high is BAD. Fish kidneys don't like it.
If you do not have carbonate hardness your biological filtration can fail.
The bacteria need the carbonate for their shells and when they die it decays back into the water. If your pH changes low too suddenly it can dissolve these bacteria as well. If your tank is overloaded you can get to a point where the bacteria consume the hardness in the water too quickly and do not decay fast enough to recycle it.
So, soft water from a softener is fine but since the ion resin takes carbonate as well as metal ions out, you should test the water to be sure it is ok to use. Water softeners are very predictable over long periods of time, so testing it only once shortly after a regeneration is fine.
Hard water may then sound like a good idea? Nope. I occasionally use straight tap water with just Prime to put iron back into the tank but I try to keep the tank around 7.8 to 8.2Kh in normal maintenance, it is a little soft but my pH rides 7.5 and higher so I know I have more carbonate. My iron actually depletes from time to time. (Carbon filters will pull it out too.)
If you drive your water hard about 400ppm your aeration will fail, nitrates over 100 will be toxic and your fish's gills will cease to operate correctly. Seen it.