A countertop kitchen receptacle circuit should have no other appliances on it. Best practice (well, NEC requirements to be fair) is to provide a separate dedicated circuit for 120V kitchen appliances like refrigerators, microwaves, dishwashers, and garbage disposals, and two or more separate 120V 20A circuits for countertop appliance receptacles, which can handle 1800w continuous load. Of course, older housing may not be wired this way.

A washing machine should never trip a breaker, if it does, there’s something wrong with the washing machine. Washing machines (typically) do not have heating elements in them, hot water is obtained from the water heater.