Catholics are as well. There are many varieties. They may still call themselves Catholics, but there are liberal Catholics, conservative Catholics, feminist Catholics, Charismatic Catholics, Tridentine Mass Catholics, etc.,
As far as continuously being in a state of fragmentation - that is NOT a basic and elementary fact, though you would like it to be. Some denominations are quite stable. Yes, they have variety within; but the Baptists, Methodists, Episcopalians, Presbyterians, & Lutherans (and others), have existed since at least the 1700s, many quite earlier.