This isn't a history discussion, GUEST, it's a discussion about where the notion comes from that Robin Hood was a crusader. The answer to that is almost certainly found in fiction, because I'm aware of every known early historical reference to Robin Hood, from the chronicles to the marginalia of government documents, and there is no reference anywhere to his being a crusader.

As for Willikin, he is one of those figures that folks desperate to find a historical figure in the reign of John seize upon sometimes as a real-life Robin Hood. However, no scholar of Robin Hood in the last half-century (or ever, as far as I know) has seriously argued that Robin Hood is based on Willikin of the Weald. The early tales of Robin Hood are about an outlaw, who is a yeoman, located in Yorkshire or Nottinghamshire, set in the reign of "Edward our comely king," or else in an unspecified time period, who fights against a Sheriff representing the duly-crowned king. Later, when moved to the time of Richard and John, Robin still fights against royal authority, though he submits to King Richard directly. First and foremost in all these tales, he is a robber.

Willikin, about whom in fact quite a bit is known, was not an outlaw, was not a robber, was not a yeoman but a petty noble or squire, was not from Nottingham or Yorkshire but from Sussex, was not in opposition to the English crown but a loyalist, and fought primarily against French invaders. He had, in other words, almost no similarity to the legend of Robin Hood, except he commanded archers and was briefly based in a forest.

As for Willikin's being a crusader, he was called a "youth" at the time of the first Barons' war (1215) by the contemporary chronicler Roger of Wendover, so he was too young to have gone on Crusade with Richard twenty years before. England didn't participate much in the fourth or fifth crusades, so his being a crusader is extremely unlikely.   

There are much more convincing "real antecedents" to the Robin Hood story, such as Fulke Fitz Waryn, Eustace the Monk, and Hereward the Wake, whom Robin Hood scholars DO see as potential sources for the tale. None of these figures went on Crusade as far as we know. Fulke, however, WAS a friend of King Richard who remained in England during the Crusade, at which time he was oppressed, dispossessed and outlawed by John, who had a grudge against him. This is most likely the source of these elements in the Robin Hood legend.