In another thread there is a discussion regarding the Tesla wipers. It appears that when the Tesla vehicle is not in Drive the wipers will stop, this would apply to Neutral. This is easy to confirm; the next time it is raining shift to Park or Neutral and confirm that the wipers have stopped. So one less thing to have to remember if you take the Tesla vehicle through an automatic car wash.
Since taking delivery of my Model Y this past June I have been washing my Tesla by hand using a soap foam cannon, 1600 PSI power washer, wash mitt and the two bucket method with a grit guard. Now that it is getting too cold to wash by hand I have switched to using Optimum No Rinse (ONR) Wash and Shine, once a week. Using ONR I can wash the Model Y, parked inside my garage, in about a half an hour. If I need to wash off road salt, when it is too cold to turn on the water to the hose bib, I plan to use the high pressure wand at the local car wash and then use ONR to finish.
Shortly after receiving my Model Y, I asked a Model 3 owner whose vehicle looked very clean how they washed their Tesla. They said they washed their Model 3 at home or at the nearby automatic car wash. They said it was their second Model 3, they never had an issue with damaging the paint, wheels etc. at the automatic car wash. I have used this automatic car wash with other vehicles I have owned, it is not a touch less wash.
My Tesla Vehicle Washing Protocol
1st year; new car - no way I would ever use an automated car wash; hand wash only
After 1st year - thinking about using an automated car wash, continuing to wash car at home
After 2nd year - might use an automated car wash in winter, otherwise continue to wash car at home
After 3rd year - would use an automated car wash, sometimes wash car at home
After 4th year - meh, who cares; do whatever is most convenient