I showed my new Tesla Model X P100D with the optional low profile 22" wheels & tires to the manager at the Soapy Joe's in San Marcos, CA; and he said it would be fine. However, I haven't taken the Tesla through an automated tunnel wash yet. However, I do take my other vehicles with smaller wheels & bigger side walls to Soapy Joe's routinely.
They do they but you should read your manual.
Don't own a Tesla, so I do not know... I'd check what your owners manual says, & also look on YouTube for possible videos which post any possible concerns related to your specific Tesla going through automated car washes.
Do they ever!
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