As for Richard I, there is absolutely no evidence of homosexuality, and quite a bit more of heterosexuality, including a number of illegitimate children and a reputation for sleeping with women while on campaign. The accusations of Richard's homosexuality stem mostly from a graduate thesis written by an Oxford historian in the 1950s, which sparked quite a bit of controversy and subsequently caught the attention of any number of authors and artists just as the sexual revolution was beginning to dawn and the view of traditional sexual roles were being challenged.

People need to stop getting their history from the movies.

Finally, though the Crusades were a humiliating calamity for European armies (only the First Crusade achieved any notable success; the others were largely failures), they must be viewed in context of the religio-militarism of the late Dark Ages and early Medieval Period, and specifically as a reaction to the Islamic Crusades that conquered Spain and very nearly conquered Europe three centuries previously.