They're called Eastern Orthodox.
Well, actually, the split was long before Vatican II, but the comparison stands nonetheless. One group refused to accept certain points of church canon that the other side accepted. In 1054 the Catholic Church split into Eastern Orthodox and Western Orthodox, or Catholic Church
https://education.nationalgeographic.org/resource/great-schism/
So, to your point, yes, this forms a different religion. They may accept or believe 85% the same, but that last 15% is the divide.
The only difference is the fans that reject Star Trek:XYZ cannot go off and make their own Star Trek. They can, however, go off and make their own show that's similar to Star Trek like The Orville, Galaxy Quest, etc...