Howdy dees,
Hope i can help you out here.
You could be in for some trouble here with this problem. Let me explain. Around the world, many cities with town water supply produce water that is hard. This hardness varies in levels of strength from city to city. The simple definition of water hardness is the amount of dissolved calcium and magnesium in the water. Hard town water can also contain various salts, minerals and fluoride.
The problem is that when you wash a car with town water, and let any residual water dry off of it's own accord on the paint surface, (especially when let dry in the direct sun on horizontal surfaces) the chemicals in the water remain and the deposits attack the paint film by chemically etching into that paint film. This etching process can be very aggressive. Water spotting is an obvious sign of chemical etching taking place.
You eliminate this problem by quickly moving in and chamois off the car before the residual water has a chance to dry on the car of it's own accord.
Always best to never wash a car out in the direct sunlight.
In regards your matte black paint being water spotted, the problem is that matte and semi gloss finishes are very sensitive paint films by their very nature.They don't like being handled in any way. They are sensitive to any form of abrasion and glossing up issues with polishing etc. Trying to remove your water spotting issue could prove to be very tricky, as the town water chemicals have etched into the paint film to some degree.
The approach i would take to try and remedy this problem would be to use soft micro fiber clothes, and first gently wipe the surface with demineralized water. Next, using the microfiber cloth again, i would gently wipe down the surface with a quality wax and grease remover. This process could help remove any salt/ mineral deposits from the paint film. I would then try to find a quality natural wax product that doesn't gloss up the matte finish. In Australia we have a brand product called Bowdens Lazy Wax.
https://www.bowdensown.com.au/lazy-wax
This is a brilliant product that features a Carnuba wax formula that does not gloss up matte and semi gloss paint finishes. Maybe you could import a bottle in from Australia, or find a similar product in the US. If that whole treatment doesn't remove or settle down the etching, then refinishing the effected panels would be the only way to remedy this problem.
Also, as mentioned above, using vinegar with a microfiber cloth could work as well to help neutalize the hard water chemicals. I have never tried that remedy myself.
Most water etching removal can be successfully carried out on most glossy paint films as you can cut and polish the etching out. As a pro auto spraypainter, i have run into trouble over the years with water etching that was not removed properly of a hood say, and painted over the etched areas. The newly painted panel played up, as the water etch marks showed through, and the panel had to be stripped down to bare metal and refinished again.
In your case, the severity of how much the chemicals have etched into your matte finish, will determine how successful you will be at removing the water spotting problem. Best of luck with that,
Greg.