The problem is where someone connected the cold to the hot and the hot to the cold. There are a couple potential remedies. The best solution is to connect the hot to the hot and cold to the cold.
Another solution depending on if the toilets are hooked up to hot and if you have certain shower fixtures with built in diverters or certain thermostatic valves.
All of the supply tubes under sinks can be swapped to correct the problem there. Most single handle shower valves cartridges can be flipped over to correct the problem there. If the toilets are connected to hot, and if you aren't solving the problem at the point of connection, then the water line would need to be swapped in the wall.