It should not automatically be assumed in church splits that the minority faction retained any rights to sue. A minority group of members may have, before suing, erased their interest by taking some action. Strangers to the church may never have had any interest.
In Dubois Street Church v Church of the Living God, Slip Op. (Mich. App. 2021), the Plaintiff was a new church entity created by former members of the Defendant church. Indeed, while forming the new church, the former members announced it on social media and invited everyone. The trial court held the Plaintiff was not the real party in interest. In other words, the Plaintiff lacked standing to assert any claim because the Plaintiff had no connection to the Defendant church. The appellate court affirmed the trial court.
A minority faction in a church split might still have an interest upon which to sue the church. But, once they proceed to form a new church and accept a new membership, and publicly announce it, that interest they had as members might be no more. Such determinations will likely turn on the record that can be submitted to a court. In the current era, that record will most likely be social media posts. In the past it might have been printed flyers or other advertisements. The lesson might be that the faction retaining control of the church should not assume the minority faction retained any membership upon which to base a lawsuit. In any event, the new church entity would have no such interest even if its members, as former members, might still have an interest.