The following is from the teaching of John A. Broadus concerning Baptists Distinctives. Baptists have always been accused of being different, and these distinctives are what sets us apart from others.
It may be well to state briefly what I understand to be the leading distinctive views of the Baptist churches. The fact that certain of these are more or less shared by others will be remarked upon afterward.
(1) We hold that the Bible alone is a religious authority; and in regard to Christian institutions the direct authority is of course the New Testament.
(2) We hold that a Christian Church ought to consist only of persons making a credible profession of conversion, of faith in Christ. These may include children, even comparatively young children, for God be thanked that these do often give credible evidence of faith in Christ! But in the very nature of the case they cannot include infants. The notion that infants may be church-members because their parents are seems to us utterly alien to the genius of Christianity, not only unsupported by the New Testament, but in conflict with its essential principles; and we are not surprised to observe that our Christian brethren among whom that theory obtains are unable to carry it out consistently — unable to decide in what sense the so-called “children of the church” are really members of the church and subject to its discipline. The other notion, that infants may be church-members because so-called “sponsors” make professions and promises for them, seems to us a mere legal fiction, devised to give some basis for a practice which rose on quite other grounds. Maintaining that none should be received as church-members unless they give credible evidence of conversion, we also hold in theory that none should be retained in membership who do not lead a godly life; that if a man fails to show his faith by works, he should cease to make profession of faith. Some of our own people appear at times to forget that strict church discipline is a necessary part of the Baptist view as to church-membership.
From The Duty of Baptists To Teach Their Distinctive Views by John A. Broadus, and from the section Distinctive Views of Baptist Churches # 1 & 2
You may read this whole study at Baptists Distinctives.
-Tim A. Blankenship