Partially open tonneau covers might prevent you from having your car washed, especially if you have some equipment in the truck bed.  The equipment might obstruct the brushes or washing equipment, and it is advised that tonneau covers should be completely closed before having the car washed. Bottom line, both soft and hard tonneau covers can go through a car wash, but it wouldn’t hurt to ask the staff whether you can take them with you or you have to remove them.