We recently saw another convertible coming out of the car wash. Fortunately the driver kept the hood closed. But let's say it again: for a (classic) convertible, the car wash is taboo because brushes and aggressive agents can damage the hood.
A car wash with rags is at most less harmful. You should in any case never have wax / wax sprayed on the hood or have it sprayed with a wax / wax program or otherwise.
The convertible top should be cleaned with water and mild soap. If the convertible is used regularly, it is advisable to wash the hood just as regularly with a mild soap. Soft soap, for example, is green soap like your grandmother used, dissolved in water.