Traditionally in the Martial Arts world, when some but not all of the students want to change how things have always been taught, there are usually only two possible outcomes:
1. Both groups claim true lineage, with the splinter group usually claiming that the master taught them the new way in secret. Everyone is confused. See Wing Chun's history for an example of this.
2. The splinter group (and sometimes even the traditional group) changes the name of their style to differentiate themselves. Everyone is less confused. The name change is usually not VERY significant, so as to show a common lineage. See the various Tai Chi styles' histories for an example of this.
So for the proponents of Parkour competition, would you be okay with not calling it Parkour? For those against Parkour competition, would you have any problems with a competition if it wasn't just called a "Parkour Competition"? Say, if it was called "Sport Parkour", "Competitive Parkour" or "Parcouring"?