In _The Stations of the Sun_, historian Ronald Hutton gives a helpful summary of the long-standing debate over the courtly vs. pagan origins of the Morris. Here's my recap:

Apparently, the pagan fertility rite theory starts with E.K. Chambers in _The Mediaeval Stage_. Hutton notes that Chambers would have been aware of the existing antiquarian theories linking the morris to courtly dance, but that he chose to ignore them, taking a more Frazerian leap of faith. Cecil Sharp then picked up on and popularized Chambers' theory, as it lent support to his idea that the dances were ancient and should be preserved in a static form. In 1957, Barbara Lowe made a detailed study of the earliest records of the morris in England, showing that it could be dated to no earlier than the mid-15th century, at which time it was clearly a court entertainment among European rulers. Lowe's findings have been supported by more recent and extensive scholarship, but were ignored by the folk dance community at the time, which held fast to Sharp's perspective until the 1970s, when more rigorous scholarly approaches were adopted by folklorists and politically more radical youth became interested in the folk dance movement.

Most scholars in the field now hold to the courtly origin theory. One exception is Sandra Billington, who suggested the "Morris" was actually just a new name applied to the older "routs and reyes" folk dances at the end of the Middle Ages.

As for the gender issue, Hutton notes that the extreme "men only" stance was championed most strongly by Sharp's disciple Rolf Gardiner (a Nazi sympathizer) rather than by Sharp himself. Indeed, although Sharp preferred an all-male tradition, he was aware of legitimately traditional 19th century examples of women dancing the Morris in Spelsbury, Oxfordshire and Blacknell, Worchestershire. Mixed and women's sides were also in fact quite numerous in 19th century Lancashire and Cheshire.

Cheers, Hester (a feminist and pagan)