When my kids were in diapers I would always put clothes on over their diapers before going out in public unless the baby had some accident and messed up their clothes and I didn't have a change of clothes to put on the baby.
I think though that unless there's something that happens to cause the child to be without clothes at that time then the child should be wearing pants, shorts or another outfit to cover up the diaper while in public.
At home in our fenced in backyard I would let the kids play outside during the summer in their diapers but when out in public the diapers were covered up.