WASHINGTON — When President Trump delivered a Memorial Day speech to the crew of the amphibious assault ship Wasp in Tokyo Bay on Tuesday, some of the nearly 1,000 sailors and Marines aboard were wearing more than patriotism on their sleeves.

At least a few service members wore round patches emblazoned with a likeness of Mr. Trump and the words “Make Aircrew Great Again” — a play on his campaign slogan — on their flight suits.

Images of the patches went viral, and the Navy soon found itself with a hornet’s nest on its hands. “They’re inappropriate & against regulation,” tweeted Mark Hertling, a retired three-star Army general.

Seemingly caught between enforcing uniform protocols and potentially getting crosswise with the commander in chief, the Navy, at least for the moment, punted on deciding whether to mete out any punishment.