The movie came out in 1984, 20 years before the not-yet-extant Nationals unveiled their "curly W" logo. Time traveler? Or something more benign? Probably time traveler.
Well, no. The third incarnation of the Senators — the one that would become the Texas Rangers — featured caps that were almost identical, from 1968 until their final season in 1971. For reference, here's a disconcerting photo of manager Ted Williams rocking the Sens' curly W.
Interestingly, one of Steinberg's commenters points out that the actor wearing the cap is named Larry Drake, the same name as a player who played four games for the Senators in 1948. When they were a different franchise. With a different logo. The plot deepens.
That said, this whole thing is less strange than if a Nats cap had appeared in the Karate Kid remake, filmed well after everyone became aware of the Nationals' follies.
A Nats hat in The Karate Kid [DC Sports Bog]