(Writing here mainly of Cotswold dances — that's the style with straw hats, hankies, bells and sticks.) Genuinely, some of the dances are "fighting dances" in that the stick movements mimic either a stylised sword fight or quarter staff fight. One or two of the dances even have names that allude to fighting, such as "Skirmish" and some are danced to military marches. These marches are not ancient tunes, though: old but not ancient.
However, the typical format of a dance is figure, chorus, figure, chorus, figure, chorus. Within each local tradition, the figures are consistent and are simple things like "back to back" and owe more to styles of social or courtly dance such as (what we now call) Playford. The chorus is what makes each dance unique. In fact, purists would use the expression "distinctive figure" rather than "chorus". So, whilst some choruses have a definite aspect of fighting to them, the dance itself does not have any sort of symbolic or representational aspect all the way through.
With a tiny number of exceptions, our dances do not "tell a story" or "represent" anything. Of course, that does not stop us saying otherwise in our hilarious introductory announcements.
As for the "two tribes" part of your speculation: the simplest response is "No." We have records of Morris dancing going back 400 or so years, and some reason to believe it is older, but it was always in the context of a small team from one village or area putting on a performance.
A lot — most, but not all — of what you would see today is a modern interpretation following a period of "discovery" collection, dissemination and revival of the dances in the very early 1900s. This was done by a coterie of educated middle class people with late Victorian sensibilities, and a whole load of ideas of "Merrie England" and "ancient pagan fertility ritual" were grafted onto something that in reality was no more than a display and a celebration.
Ask anyone with an interest in the subject and they are likely to tell you that Morris was danced by farm workers on May Day to encourage fertility in the crops. However, the Morris was "discovered" by Cecil Sharp on Boxing Day 1899 being danced by out of work labourers hoping to raise a bit of money.
There are other forms of Morris dancing from various regions of England and Wales and the differences are so fundamental that it is clear that they had different origins. While many of them could be seen as a display of overt "masculinity" (lots of clashing of sticks or metal blades, or stomping of clogs) none of them could reasonably be seen as a surviving fighting ritual as a replacement for actual warfare. ("Masculinity" in quotes because these days, more than half of Morris dancers are female.)
Vardoger: this may be a longer and more pedantic response than you wanted, but as a Forteans, I am interested not only in "what ifs" but also in how easy it is for us to let our preconceptions and whimsical speculations lead us not only beyond the data, but sometimes in the opposite direction. The common thread of much of Forteana is that we would all like it to be true, whether it is in a pet theory, a pagan survival, an anomalous phenomenon, or a cryptid.