There are various schools of Islamic philosophy, sure, but I thought those were less important in Islam "how she is practiced" as the schools of jurisprudence (Hanafi, Maliki, etc.) and certainly don't involve mutual hostility on the level of Catholics and Protestants OTL (or, for that matter, different protestant sects in the first couple centuries after the Reformation). [1] A Zahiri scholar need not fear being burned at the stake if he travels into Ashari territory. (Do they even have "territory"? I know schools of jurisprudence have certain geographic areas where they prevail, and I'm seen maps, but I've never seen such a thing for schools of philosophy).
[1] Modern "purists" on the Salafi model being something of an exception.