Carpets of actively bending cilia can exhibit self-organized metachronal coordination. Yet, active noise of the cilia beat is expected to perturb cilia synchronization. Using a multi-scale model calibrated by experimental cilia beat patterns, we find local multi-stability of traveling wave solutions. Yet, a single dexioplectic wave has predominant basin-of-attraction. Beyond a characteristic noise strength, we observe an abrupt loss of global synchronization even in finite systems, characterized by local synchronized patches. This theory prediction matches experimental observations in the ciliated nose pit in zebrafish.