They do, however, each have specific specifications for their coolant. Do you happen to know which specific type of antifreeze meets the mazda specifications?
I don’t know what mazda requires, but I don’t begin to believe the application information from the antifreeze manufacturers. For example, Valvoline lists it’s “Zerex DEX-COOL” for late model mazdas, here:
http://www.valvoline.com/zerex/pdf/Zerex_CoolantChart.pdf?coaid=1B5D1AEA1AFC