I think it's good for children (people in general) to be comfortable in as many situations as possible.
It's hard in Covid times, but I have never been afraid of hospitals, for example, as I had to visit elderly relatives as a child, and had to go quite a lot myself, so stroll in fairly confidently even if I need medical attention.
I'd take them to church, maybe several, even if you don't believe, occasionally. It will make attending a funeral, or perhaps a wedding, less daunting if they've been through the door and seen what goes on.
Also to court - trials are public in England. A visit to the Old Bailey, preferably the older one, is very interesting and gives real insight into the expected behaviour, even down to an absolute ban on mobile phones. Better for older DC, say mid-teens. The staff member directed us to the most interesting trial and explained how to enter (quietly, difficult as the old wood floor creaks!).
Another for secondary age would be parliament. Contact your MP who will arrange for you to get in. It's popular, so you need to apply months in advance, specially to hit a time when it's sitting but the DC aren't in school.
The more DC are used to being in these formal settings, the more confident they will be in approaching the next one.
Another good visit is the Cast Room at the Victoria and Albert museum. Partly to see the items, but partly to explore the concept that in Victorian times the average member of the public had no chance of seeing the original Trajan's column or the facade of Santiago de Compostela Cathedral, etc, etc, and how amazed they must have been to see the copies. We now have Google to give us information about why things are considered important.