Following yesterday's post, Professor Bainbridge directed me to a 2007 article that he co-wrote with Aaron Cole, The Bishop's Alter Ego: Enterprise Liability and the Catholic Priest Sex Abuse Scandal, 46 J. Catholic Legal Studies 65 (2007).  The article notes that the corporation sole isn't the only entity option available for religious organizations:

"American corporation law offers religious organizations a number of statutory forms through which they can gain 'legal recognition, status and rights, particularly the right to acquire and hold property.'   Among these are the unincorporated
association, the charitable trust, a not-for-profit corporation, a religious corporation, and the corporation sole."

Id. at 75 (footnotes omitted).  The article also explains that American Roman Catholic Bishops likely favored the corporation sole as a response to trusteeism:

"In the mid-nineteenth century, some lay parishioners claimed that then-existing laws under which their churches had been incorporated granted the lay members of the church parochial administrative powers and even the right to choose and dismiss pastors. In 1854, “'trusteeists, conspiring with newly elected state legislators of the anti-Catholic Know-Nothing Party, procured in New York, Pennsylvania, and elsewhere laws intended to compel all Catholic parishes to adopt the . . . trustee form of incorporation,' which would have imposed Congregationalist (democratic) polities on the Catholic church despite the clear hierarchical structures mandated by Church teaching."

Id. at 76 (footnotes omitted).  It should be remembered, however, that the corporation sole is not limited to the Roman Catholic faith and is available to any "religious denomination, society, or church".  Cal. Corp. Code § 1002.