No. Not all Lutherans are the same for not all Lutherans teach or practice according to what God says in His Holy Word, the Bible.
The three largest Lutheran Church bodies in North America are the Evangelical Lutheran Church in America (ELCA, www.elca.org), the Lutheran Church—Missouri Synod (LCMS, www.lcms.org), and the Wisconsin Evangelical Synod (WELS, www.wels.net). Visit their respective Question/Answer pages and you will find a great deal of difference between ELCA and the other two.
ELCA fundamentally has a different understanding of the Gospel, Holy Scripture, the Lutheran Confessions, and the Sacraments than do the others. If the definitions or explanations given by ELCA sound similar, it is only because they use similar words, but with entirely different meanings (meanings and usage which are foreign to Holy Scripture). In practice, these differences clearly show themselves (i.e. the ordination of unrepentant homosexuals and of women, contrary to the Lord’s mandate; the toleration and acceptance of behavior contrary to God’s will; fellowship with “Christian” church bodies that teach doctrines contrary to God’s Word [open communion]; worship nonChristians [i.e. Jews, muslims, etc.], and not least of all, preaching which is devoid of the vicarious satisfaction of Christ, the forgiveness of sins, and eternal life through faith in Jesus [the preaching that unrepentant (nonbelieving) sinners are saved is ever increasing].
By far, the doctrine and practices of the ELCA are quite distinct from LCMS and WELS. However, between the latter two, noticeable differences do exist.
LCMS permits women to vote in congregational assemblies. WELS does not. LCMS permits its young people (and even encourages in some cases) to join boy/girl scouts. WELS encourages it young people to participate in a WELS group somewhat similar to the scouts. LCMS has military chaplains. WELS has civilian chaplains, but no military chaplains. Also, LCMS and the WELS have a different teaching of The Office of the Ministry and its relation to the priesthood of all believers (however, in practice, differences are not so readily recognizable due to the fact that the LCMS seminaries and colleges in the Concordia University system of the LCMS do not consistently teach similarly, nor are pastors and laypeople always so clear on the distinctives).
LCMS and WELS both accept the Bible (both Old and New Testaments) to be God’s Word (and without error) and the only “rule and norm for faith and life.” Both also subscribe unconditionally to the Lutheran Confessions. The ELCA does not accept either the Bible or the Lutherans Confessions as the LCMS and WELS do (if the ELCA does in word, then certainly not in practice).
Both LCMS and WELS also clearly teach Christ and Him crucified as the only means of salvation (1 Corinthians 1:23; 2 Corinthians 4:5). The ELCA is not clear on the genuine Gospel of Jesus Christ and fails to distinguish between what is sin before God and what is not.
There will be exceptions to the above comparisons. ELCA pastors and congregations who seek to be more faithful to the Bible than their church body as a whole do exist. In the same way, LCMS and WELS pastors and congregations exist who do not teach and practice according Holy Scripture and the Lutheran Confessions (i.e. using worship practices and innovations that are foreign to biblical doctrine).
Simply because someone says that they are a member of an ELCA, LCMS, WELS, or other Lutheran Congregation does not immediately mean that they are genuinely Lutheran. Nor does the word Lutheran attached to the name of a church body immediately indicate that the church body is genuinely Lutheran. Only by discerning according to Holy Scripture and the Lutheran Confessions is one able to make such a judgment.