Good manners are snobbish?
I think you don't understand the word "breeding" as it was used in the context it was. You keep equating the quoted meaning of breeding with procreation and the definitions are not related.
I've read all the posts and I think the original posters hesitancy on attire at the Brown Derby was spot on. I too would be uncomfortable in the Brown Derby if I didn't dress a bit nicer than I would for a nicer restaurant regardless of what anyone else chose to
I do understand the multiple meanings of the word "breeding." Given the poster's use of the word "upbringing," there was no need to add in breeding, which most definitely gives off a different connotation than that which may have been intended.
Regardless of what you would feel comfortable in, the OP asked if park attire would be appropriate to wear in the Brown Derby; the answer to that is yes, since that is what most people do.