A minister upon producing to the secretary of state, credentials of the minister’s being a regularly ordained or licensed minister of any religious society or congregation, shall be entitled to receive from the secretary of state a license authorizing the minister to solemnize marriages in this state so long as the minister continues as a regular minister in that society or congregation. A minister shall produce for inspection the minister’s license to solemnize marriages upon demand of any party to a marriage at which the minister officiates or proposes to officiate or upon demand of any probate judge.