I grew up in Kansas in the 1980's and heard sort of 3rd hand family lore about the homesteads from 100 years prior. I'm going to set much of that lore aside as our family embraced both for various reasons.
You wouldn't think it, but one of the major feuding points came down to something a simple as a piece of wire. The invention of Barbed Wire (along with the near destruction of the North American Bison) changed the nature of homesteading in the Great Plains. Oddly enough there are several good books on the subject, some of which are out of print and I'm unfamiliar with a few of the newer ones, but both appear available on Amazon if you want a deeper dive into the history of the wire.
I'll try to summarize the nature of this conflict. First, a few words concerning the Great Plains area in general. The early to mid 19th Centruy the Great Plains had vast heard of Bison/Buffalo that roamed the plains and were a major food and material source for the Native Americans in the area. In the mid 1800s Kansas and Nebraska began to see an influx of mostly white, European settlers that began to put pressures on the Natives and the Bison. The systematic elimination of the Bison was seen as a strategy for "pacification" of the Native tribes.
The near-elimination of Bison opened up an enormous amount of acrage for free range cattle and for homesteading farmers. Without the Bison to compete for grassland cattle herds thrived in the open sea of grass. Without giant herds of Bison roaming free, homesteaders had less fear of crop destruction from the larger animals (not to mention a reduced fear of attacks from angry Natives). This did however lead to a conflict in interests. Cattlemen preferred larger open ranges where cattle could feed off of plentiful grass and be freely driven to a railhead over open ground/trails. Homesteading farmers could parcel out the land and claim ownership (via the Homesteading Act). The farmers would tear up the grass and break up grazing areas for the cattleman. In turn, the cattleman would be indifferent to or even encourage their herds eating or trampling farmers crops. This would naturally lead to some hard feelings and conflict.
This is where barrbed wire comes in. One way to easily mark out homesteaded ground was to put up fencing. East of the Plains, wood is in plentiful supply so rail or rail/stone fences were fairly common and sturdy ways to keep fields safe from free-range (and wild) animals and contain farm livestock. Bison are capable of destroying all but to most sturdy fencing, even by modern standards, so their removal did help in areas where fencing supplies could be had. Further out into the plains, wood for fences is a very scarce item. Wire fencing became a solution. Posts could be made from wood and/or stone and the spaces in between would be strung with wire or a wire mesh. This usually works for smaller animals, but very well for cattle and larger farm animals. Barbed wire became the solution. The barbs/thorns on the wire would deter cattle from pushing/rubbing a fence down. This works rather well on domesticated cattle or at least cattle that get acclimated to it.
The wire gave homesteaders a potent weapon in the war on the the range. Free range cattle could now suffer serious injury blundering into a barbed wire fence. Cattlemen/cowboys would come and cut fences to allow their cattle to cross homestead grounds.
Eventually over the Nortern and Central plains ranges became more and more restricted and closed. Large herds were broken down into smaller ranches that would occupy ranges were the soil was less conductive to farming.
Oklahoma managed to stay more free range and open during this time as the area was considered "Indian Territory" and not available to Homesteading settlers. Oklahoma was not technically available to white homesteading until 1889. This began the closing of the larger and last open range areas in the Great Plains. While there are to this day large areas of untitled grassland in the Great Plians, the era of free open range grazing came to an end. This did not exactly end the conflict between farmers and ranchers as grazing rights, water rights, land usage, and fencing continued to cause friction into the 20th Century. Throw in a generation or two of bad blood between neighbors and it wouldn't be too hard to see how this made it's way into a musical about the era.
A quick word on the background for the Musical as well. The dustbowl of the 1930s sent many of the sons and daughters of the original settlers of Oklahma on desperate trips to California that often made it's way into contemporary writings of that time (Grapes of Wrath, Of Mice and Men readily come to mind). It shouldn't be much of a surprise that along with that there would be stories from their parents generation of what the early days were like and a nostalgia for what was lost in the drought. Combine that with some catchy songs by the top Musical duo of the era and it's no wonder Oklahoma was a success.