Gentlemen, apologies if I have offended. However, I do believe you've mis-interpreted the general tack here. Both of these are examples showing the baseball style cap as part of a uniform. I'd wager that neither of the gentlemen in question wore/wear it where inappropriate.
a)It would be against regulations to wear a casual cap to a 'Class A' function.
b)I doubt the gentleman in law enforcement would wear his duty cap to a 'Policemen's Ball'.
My grandfather worked the railroads for 40+ years (after returning from the war) and frequently wore a baseball style cap in the summers, and wore whatever he could to keep himself warm in winter, HOWEVER, apart from fishing, you'd never see him in that style of cap.
A Gentleman is aware of his situation and surroundings, and dresses to best meet them. Wearing a baseball cap (which isn't part of a uniform or workwear

) indoors, at meals, etc, etc, IS inappropriate.
Unfortunately, the baseball cap is quite nearly the only style of cap to be found these days. Everything else, presumably, is a hat.

It may be a tradition, but only in it's proper place. Everywhere else it's a fashion no-no.
A brief summary of the term 'Chav' can be found
HERE.
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