> As an example Frigidaire, GE, KitchenAid, Whirlpool will only work with hot water
Yeah, afaik without actually looking into it, of those only Whirlpool is distributed here (KitchenAid stuff yes for sure, but not I think dishwashers) and as above I'm pretty sure they must be different models, just like LH/RH driver cars.
Of course you can import whatever you want, but then you should probably expect to deal with some such plumbing (and potentially electrical, at very least changing the plug) oddities.
In the US, it's common to have a water softener on the hot water line, intended to soften the inputs for appliances and showers. The cold water line is not softened, to avoid drinking sodium-laced water.
I don't claim authority on the matter though.
As an example Frigidaire, GE, KitchenAid, Whirlpool will only work with hot water; Samsung, Ikea, Beko will only work with cold water; and Bosch, Miele, Electrolux, LG will work with either.