What causes a Mazda to overheat quickly when accelerating with a new water pump and thermostat and radiator and no oil in the water or water in the oil or steam out the tailpipe or water loss?

Most likely considering the new thermostat is OK, you have a badly kinked, or twisted hose, or a clogged heater core. To check flow is good; After wam-up, squeeze top, bottom or both (one than the next) large hose, and feel for flow, it also should feel warm. Upon release, you should hear a squishing sound. Also, you can have a loose belt that drives the water pump. Tom