Not crusaders but Englishmen
Accoding to Polydore Vergil
[Edward III] appoynted his souldiers to wear white Coats or Jackets, with a red Crosse before and behind over their Armoure, that it was not onely a comely, but a stately sight to behold the English Battles, like the rising Sunne, to glitter farre off in that pure hew; when the souldiers of other nations in their baser weedes would not be discerned.
So the whole St George cross thing has nothing to do with crusaders (kicking the crap out of the muslims, and then having the crap kicked out of them a few decades later), and more to do with the 100 years war (kicking the crap out of the French, and then having the crap kicked out of them a few decades later).