"It's so famous that my friends on the other side of the Pacific are asking me about this," fan Mob Liu said on Facebook.
A Facebook vendor who sells the patches said he has received around 1,000 orders since the image went viral on Saturday.
Most of the requests are from Taiwan but order requests have also been received from China and Hong Kong.
"The people of Taiwan are disgusted with China's overacting military exercises after the Tsai-McCarthy meeting so this pilot's badge sparked discussion," said the Facebook vendor, who asked to be identified by his business name Wizardgeo.
"The people support the military in defending our sovereignty."