Shoes, along with Socks, are pieces of the Paoli 1 Uniform that is not standard issue. When in uniform (even Class B) scouts have hiking boots but the brand, style, and model are up to the individual scout although advice is always available regarding a new boot purchase. Although the boots are not uniform, they must be presentable just like any other part of the uniform. That means they should be reasonably clean, laces should be intact, they should be tied, etc.

When not in Class A or Class B, scouts have complete freedom in their dress and that includes their footwear.
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Matt Bilker's Vasque 2.0 hiking boots

Certain events will request special footwear (e.g. River Trips) and several Class A or B events may specifically vary from the boot in favor of a sneaker (e.g. First Aid Meet).

Although scouts might often be free to wear what they please on their feet, the are rarely permitted to go barefoot for safety reasons. This rule generally only comes up at Camp Horseshoe where the scouts are more inclined to kick off their shoes in the warm weather. Scouts should only be barefoot in the Pool or when in their own patrol pavilion back at Lisle.