I saw this on Facebook tonight, and it reminded me that Memorial Day is this Monday, the unquestioned start of the summer clothing season, which includes straw hats.
One-hundred years ago (and much more recently), Straw Hat Day was an official thing, often proclaimed by the mayor of a given town sometime in April; often it was either May 1 or May 15, but sometimes as early as Easter (especially in the South, where the weather warms sooner).
But no-one will question that it's okay to wear things like straw hats (and white bucks, seersucker, etc.) on Memorial Day and after. (Although apparently a May 20, 1908 editorial in the New York Times pegged Straw Hat Day as June 15.)
Unfortunately, wearing any type of dress hat in 2017, especially with a suit, will cause many to look at you askance, so don't obsess over this stuff too much; it's mostly arcane historical trivia at this point.
But don't wear your straw hat until Monday. 😀