From the FAQ section of the LCMS website:

Q. What is the Synod's view of membership in lodges, fraternal organizations and fraternities?

A. It has consistently been the position of The Lutheran Church--Missouri Synod throughout its history that membership in the Masonic Lodge is incompatible with membership in a synodical congregation. Article X of the bylaws of the Synod outlines the scriptural rationale for this position and the pastoral procedures to be followed in dealing with uses of lodge membership. The Commission on Theology and Church Relations has prepared a detailed discussion of the reasons for the Synod's opposition to membership in the Ancient Free and Accepted Masons.  You may read this evaluation online.

There are fraternal organizations (e.g., Kiwanis, Lions Club) or community clubs that do not have the objectionable features of the lodges in their rites, ceremonials, and membership requirements. There are generally no objections to membership in such organizations.

Since there are so many college fraternities, and since their membership requirements vary, the Synod's Commission on Theology and Church Relations has advised that judgments must be left to individuals based on the particular case.

Of God

4. On the basis of the Holy Scriptures we teach the sublime article of the Holy Trinity; that is, we teach that the one true God, Deut. 6:4; 1 Cor. 8:4, is the Father and the Son and the Holy Ghost, three distinct persons, but of one and the same divine essence, equal in power, equal in eternity, equal in majesty, because each person possesses the one divine essence entire, Col. 2:9, Matt. 28:19.  We hold that all teachers and communions that deny the doctrine of the Holy Trinity are outside the pale of the Christian Church.  The Triune God is the God who is gracious to man, John 3:16- 18, 1 Cor. 12:3. Since the Fall, no man can believe in the "fatherhood" of God except he believe in the eternal Son of God, who became man and reconciled us to God by His vicarious satisfaction, 1 John 2:23; John 14:6. Hence we warn against Unitarianism, which in our country has to a great extent impenetrated the sects and is being spread particularly also through the influence of the lodges. {Emphasis added.}

The entire “Brief Statement” may be viewed at the Project Wittenberg site: www.iclnet.org/pub/resources/text/wittenberg/wittenberg-msynod.html

From a doctrinal essay titled, "WHEN DO WE USE THE DOCTRINE OF THE CHURCH PROPERLY?" by Professor Theo. Hoyer.  This essay was given June 15-19, 1942, at the 41st Convention of the Minnesota District of the Evangelical Lutheran Church of Missouri, Ohio and Other States at St. Paul, Minnesota.

"It’s sadly true that men will rather believe evil than good of their fellowmen; and I need not go to any length to prove that pastors are even more than others the victims of that propensity; and there are only too many church members who think, when a pastor is slandered: Where there is so much smoke there is bound to be some fire. Untold harm is done the Church by that sort of cowardly action.  Let no Christian be ashamed of his pastor when people throw filth and spit poison, and the newspapers drag his name in the dirt, because he testifies against lodges, or against prevalent sins, or refuses to bury everything that’s dead.  Let us back up our pastor under such conditions; and share his dishonor, which is an honor to him and to his backers in God’s sight. " {Emphasis added.}

The entire essay may be viewed at www.confessionallutherans.org/papers/hoyer.html

From the LCMS Committee on Organizations (COO) report on the Order of Elks:

"Although the Order has less emphasis upon religious philosophy in its ritual than Freemasonry, nevertheless the principles of the Order are promoted as meriting the approval and blessing of God.  The Order is to be commended for its patriotism and its benevolent contributions to society.  The sincere Christian will, however, be concerned that his desire to approach God only through Jesus Christ is ignored, in spite of the fact that he had been promised there would be nothing to conflict with his religious convictions. He obligates himself not to introduce at Lodge meetings anything of "sectarian character" only to discover that whole ceremonies are built upon the sectarian premise of universal salvation which he cannot accept.  If used, the poem "Thanatopsis" confuses him since it denies all immortality, while ritual references give assurance of immortality.  He hears of the "redeeming grace and power" of God, but sees it applied to men who reject the Redeemer. As a Christian he believes that his good works do not merit God's approval but are simply a response of thanksgiving and love to God for God's gift of salvation in Christ. (1 John 4:19) Yet at the graveside of a brother Elk he hears that observing and advancing the principles of Elkdom merit God's blessings and approval.  The Christian is further disturbed when the Bible is used only as a Book of Law, certainly a lesser purpose than that for which it was given--to make men "wise for salvation through faith in Christ Jesus." (2 Timothy 3:15)  Evaluated on the basis of the fundamental doctrines of the Christian faith, the religious themes in the Elks' Ritual--the prayers, hymns, funeral and memorial services--are incompatible with confessional Christianity. Officers of local Elk Lodges sometimes insist that some rituals are omitted and that funeral services are falling into disuse.  Whether omitted or not, however, these forms still define the Elks' religious philosophy. Initiated members obligate themselves to these and all other ritual forms. Membership in the organization would compromise the public profession of a Christian's faith, something which he cannot do in good conscience." {Empasis added.}

The entire report may be viewed at the LIL page COO on Elks.