According to the 1945 charter amendment the Watchtower is a non-stock corporation with only voting shares.
The voters are selected by the board and have to be dedicated male witnesses.
If they elected non-JW's the Watchtower board would be violating the charter, and for this there can be serious consequences:
First, there is a doctrine called ultra vires. It is a Latin term that essentially means that acts outside the permissible scope of authority set forth in the governing documents is unauthorized activity that cannot be ratified by the board. As an example, if a nonprofit enters into a contract that is outside the scope of its permissible activities, the contract could be voided. While there may be other arguments that could be raised to enforce an ultra vires contract, acting “ultra vires” puts the nonprofit at risk as well as those that are entering into transactions with it.
Second, if directors act in ways that conflict with the nonprofit’s governing documents, they may be opening themselves up to an argument that they are breaching their fiduciary duties including the duty of due care and the duty of obedience. In most states, fulfilling one’s fiduciary duties is a prerequisite to a statute that basically says the board members can’t be held personally liable for their mistakes so long as the mistakes were made in good faith, out of loyalty and obedience to the corporation, and with due care. By failing to fulfill their fiduciary duties, the directors risk personal liability for any harm caused by their actions.
Third, if the directors are ignoring the rights of the nonprofit corporation, most states have a process that permits a group of directors (or voting members in a membership corporation) to get together to bring a derivative suit on behalf of the corporation. In the nonprofit context, a derivative suit is a law suit brought by a group of directors or members against a third party. That third party can be another insider such as another director or group of directors. These suits are brought from time to time when relations break down and factions form on the board of a nonprofit.
Fourth, the typical saviors for wayward nonprofit officers and directors, D&O insurance and corporate indemnification, won’t save directors who act outside the scope of their authority. D&O policies typically exclude ultra vires acts from coverage and corporate indemnification is generally not available to those acting outside the scope of their authority.
from: http://charitylawyerblog.com/2010/07/14/nonprofit-law-jargon-buster-ultra-vires-acts/