Can you explain why not? It appears to be entirely consistent with the criteria you're using for "whateverism".
Dictionary.com Unabridged (v 1.1) - Cite This Source - ---
schism Audio Help /ˈsɪzəm, ˈskɪz-/ Pronunciation Key - Show Spelled Pronunciation[siz-uhm, skiz-] Pronunciation Key - Show IPA Pronunciation ---
noun 1. division or disunion, esp. into mutually opposed parties. ---
2. the parties so formed. ---
3. Ecclesiastical. a. a formal division within, or separation from, a church or religious body over some doctrinal difference. b. the state of a sect or body formed by such division. c. the offense of causing or seeking to cause such a division. ---
[Origin: 13501400; < LL (Vulgate) sc(h)isma (s. sc(h)ismat-) < Gk, deriv. of schízein to split, with -ma (s. -mat-) n. suffix of result; r. ME (s)cisme, sisme < MF < LL, as above] ---
schism n. A separation or division into factions. ---
A formal breach of union within a Christian church. The offense of attempting to produce such a breach. Disunion; discord. ---
[Middle English scisme, from Old French, from Latin schisma, schismat-, from Greek skhisma, from skhizein, to split; see skei- in Indo-European roots.]