What makes you think those components are isolated from ground? The solenoid in your picture has a metal mounting plate that gets mounted to the metal frame of the dishwasher. An overheating solenoid will eventually create a ground fault tripping a GFCI breaker. It will probably never pull enough current to trip a standard breaker.
While I don't agree with some of the new requirements for GFCI protection, especially central A/C equipment, in most case there will not be any issues other than the cost of the GFCI.
I have not had any call backs on projects we have wired due to dishwashers and disposals tripping GFCI's.
Commercial kitchens have required GFCI protection for a long time now without major issues.
Both the service manual mention no ground and the actual machine has no ground over to the drain valve. The solenoid body is metal yes, but mounted to a plastic pump body:
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This is the reason why new dishwashers rarelly if ever trip GFCIs, they were redesigned to isolate most major components.