Corrected entry: Throughout the entire movie, Parkmans' helmets never have a protective piece covering the ear. Any baseball games at any level the helmets have that protective piece over the ear.
Correction: MLB made it mandatory for batting helmets to have at least one earflap in 1983. Players who were already using non-earflapped batting helmets up until that point had a grandfather clause, so they could keep wearing those if they wanted to. I guess we have to assume Parkman has been playing since before 1983.
Correction: This is USUALLY true but not entirely, especially in the 80's. I remember several of my favorite players, including then Chicago Cub's catcher Jody Davis, wore the same kind of helmet and I used to wonder that myself. Rare yes, but not unheard of.
John Olrud wore that same helmet as well when he played in late 80's, early 90's.
John Olerud wore a helmet without earflaps in the field. He batted with a helmet that had earflaps.