My side of a recent Facebook exchange:
Why don't we drop the 41K denominations figure. That's highly misleading. Most Christians belong to handful of major denominations, viz. Baptist, Presbyterian, Anglican, Lutheran, Wesleyan, Pentecostal. You might say there are different Baptist or Presbyterian denominations, but these are families of denominations. They often have identical theology. The substantive distinction is between confessional/conservative and progressive Baptists, Presbyterians, &c. Most Christians belong to a handful of larger denominations that represent a historically stable package of theological beliefs. Even independent churches are apt to have a doctrinal stance identical to one of the standard denominations. These distinctions are necessary to correct a Catholic apologetic trope against sola scriptura and "pervasive interpretive pluralism".
This trades on equivocal usage regarding what constitutes a denomination. Do we count all Baptist denominations as separate denominations or as representatives of the same faith tradition? It's really a species/subspecies distinction.
Once again, I already anticipated the distinction between confessional/conservative denominations and progressive denominations, so you're objection is behind the curve. While local Baptist churches are technically autonomous, what makes them Baptist is affiliation with a particular faith-tradition.
I also don't know what you mean by "this is how chaos happens". Denominations that don't have autonomous local churches, denominations that are technically confessional and have a degree of hierarchy (e.g. Anglican, Lutheran, Presbyterian) can also liberalize. There's nothing about Baptist polity that makes it more susceptible to theological drift. That's easily paralleled in denominations with a more authoritarian polity.
Once more, the doctrinal requirements for elders are naturally stricter than for laymen since elders are the primary teachers and doctrinal enforcement officers. How is that germane to the rubbery 41K figure?
"I am not the one counting, I am simply using sources. So you will have to take it up with them."
I don't concede your fallacious argument from authority. We're discussing a substantive issue, and not how a reference work happens to list churches or denominations.
No denomination has a more elaborate authority structure and accountability system than Roman Catholicism, but that hasn't preserved it from "chaos" over the centuries.
You've now made clear that you have an antagonistic agenda regarding autonomous churches. That's your prerogative. You then use that to prop up a standard talking-point used by Catholic apologists. That may not be your intention but that's the effect.
But the attack on autonomous churches is invalid since there are parallel problems in churches with a more structured polity. So your objection is inconsistent.
There is no "simple fact". There's no one criterion or set of criteria to classify denominations and faith traditions. You have chosen to focus on the most superficial.
Yes, Baptists split. So do Anglicans, Lutherans, Presbyterians, &c. A particular polity is not a safeguard against schism or institutional apostasy.
i) Your response is confused. I wasn't commenting on your post but your statement to Vlad about 41K denominations. You are undeniably antagonistic towards "autonomous" denominations.
ii) It's hardly frivolous to point out that your arguments in that regard are inconsistent. "Autonomous" denominations split and/or liberalize, but so do more hierarchal denominations. The UMC is about to split over homosexuality, and it split in the 19C over slavery. Yet it has bishops.
iii) It's not frivolous to point out that there are different ways to count Protestant affiliations. For instance, you can count them by faith traditions or denominations. Denominations typically exemplify particular faith traditions. It's a one-to-many relation. So do you count Baptists (or Methodists, or Presbyterians, or Lutherans, or Pentecostals, or Anglicans) as one each, according to the faith tradition they share in common, or do you count them as so many separate denominations? Likewise, if denominations group into theological families, do you count them as individuals or families?
That's not frivolous. Rather, that's a theologically and philosophically discriminating analysis. And it's not asking too much that an apologetics forum operate according to high standards of rational analysis.