I have the same problem with water in Perth, Western Australia. The tap water here is toxic regardless of what the water corporation says. We get a white residue left over after water evaporates and it is not anything I can pick up with a GH or KH test kit and it does not raise the pH.
Our tap water is very soft (GH less than 50ppm) but very alkaline (pH above 8.0).
If it add tap water to methylated spirits (ethyl alcohol/ ethanol) the alcohol goes green. If I add bottled or distilled water to the alcohol it stays clear like it is meant to. I use methy to clean things, not to drink.
I did various tests with our tap water and even had the water corp come out and test it too. Their results were the same as mine, basically 0 ammonia, 0 nitrite, 0 nitrate, low GH, no KH and high pH. They also did a chlorine test and found we had 3.5 times the safe level of chlorine in the water. Safe level being no more than 2ppm and ours was 7.5ppm. They said to aerate the water for 24 hours or leave it out in the sun for a few hours to remove the chlorine. That didn't help.
I use to vigorously aerate my water for a week before using it, and I added a dechlorinator at recommended dose rates, and a Rift Lake water conditioner at half strength. My water holding tanks also had undergravel filters in them. This was the only way I could use my tap water on the fish I kept. I had a range of fishes including Australian & New Guinea rainbowfish, various Corydoras, South American and African dwarf cichlids from soft water, and dwarf cichlids from Africa's Rift Lakes. I also had a number of native species that are not available from shops.
Whilst a lot of these fish came from soft water, they died if I did not increase the GH of the water I used. They were fine in the hard water but perished rapidly (within days) if I used soft water. They start breathing heavily and die an hour or so after they started to breath heavily. We put this down to a chemical/s in the water and by increasing the hardness (using the Rift Lake conditioner), the minerals were able to bind with the chemicals and help make them less toxic to adult fish.
I did tests using the same water, (aged for a week with Rift Lake conditioner, etc) and the water killed rainbowfish fry as they emerged from the eggs. So whatever was in my water, and is still in it, is lethal to baby fish, and pretty much anything aquatic. However, by increasing the general hardness to over 200ppm, I was able to keep a variety of adult fishes.
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Depending on how hard your water is, you could try increasing the GH and see if that helps. Alternatively look at reverse osmosis (R/O) units and see about trying that. R/O units do waste a lot of water but they give almost pure water. Another options is to buy a couple of inline filter cartridges and connect them to your tap. The first cartridge can contain a material filter to screen out dirty and sediment, and the second cartridge can have activated carbon in to remove chemicals and heavy metals. The carbon will need to be replaced regularly but it might help.
If you don't have the resources for inline filters, try aerating your tap water in a bucket for a week and have a carbon filter in it. Fill up a large plastic container or bucket, add dechlorinator and aerate vigorously. After 24 hours add a box filter with activated carbon in and leave it to run for a week and then use the water.
Aerating the water and conditioner for 24 hours will get rid of any chlorine in the water and when you add the carbon after that, it can absorb any heavy metals or remaining chemicals from the water. It might help.