I have seen threads on TMC re the discoloration problem on the Model Y trim. I would find out what the black trim on your Model Y is made of. The problems you referenced occur if the trim is made of anodized aluminum and the car is cleaned with a high pH (alkaline) soap. Because touchless car washes do not make any contact, they typically do not clean the car as well. To increase their cleaning ability, touchless car washes typically use high pH soaps. Anodized aluminum should never be exposed to a high pH soap.
Personally, I would never use a touchless car wash. Not only would the high pH soap possibly damage your anodized aluminum trim, it can also degrade or remove car waxes and sealants. If you must use a touchless car wash, I would contact the owner and first find out if they use high pH soaps.
For example, this is copied from a wikihow article on how to clean anodized aluminum:
"Pick a neutral cleaner. The best cleaners for anodized aluminum are in the pH range of six to eight. Seven is neutral (as opposed to acidic or alkaline), so you want cleaners that are close to neutral. Anything too acidic or too basic can damage the surface.
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If you have anodized aluminum trim, as long as you wash your car with a pH neutral soap, your trim should be fine.