By utilizing MacIntyre's definition of a tradition, Stout is attempting two projects: (1) redeeming democracy from resentment and (2) trying to create space for the role of religion in democracy. Stout identifies two camps of resentment. First, those who resent religion for the corrupting influence that it has had in democratic societies. Richard Rorty argues that because of this corrupting influence, religion in general and Christianity in particular should be kept private -- for the emotional and spiritual health of its devotees -- but it should be kept out of the public sphere. Rorty calls this the "Jeffersonian Compromise". Thus, Rorty wants to draw a hard boundary line between any religious tradition and the democratic tradition. (See Rorty's Philosophy and Social Hope.) Second, there are those who resent democracy because of its corrupting influence on the church. MacIntyre and Stanley Hauerwas both argue for a hard boundary line between the democratic tradition and the Christian tradition in order to keep the state from corrupting the church. Stout maintains that these two "theologies of resentment" have gone too far and that there is a place for religion in the public square.
Stout begins defining democracy as a tradition by arguing that the LDT starts with a minimal form of government in which the adults have access to participate in electing rulers and can contribute to legislative conversations. Stout thickens his definition of the LDT by arguing that this form of government also includes moral norms that guide our obligations to others in society. Some of these norms are located in the Bill of Rights, some are located in our principles of due process and others are surfaced in the giving of and asking for ethical reasons. For Stout, all this requires two key virtues of "tolerance" and "respect for others". Thus, Stout's thick democratic tradition (LDT) includes: sacred texts (The US constitution, the Bill of Rights), authority figures and exemplary examples in Emerson, Whitman and Dewey, a vision of the good life (peacefully accommodating the diversity of pluralistic cultures in one society) and practices (giving and receiving of reasons) necessary to cultivate the virtues (humility, charity toward others). His account of LDT creates space for other traditions to flourish, as long as they are bounded by the minimal practices and principles of participation–the giving and receiving of reasons in moral discourse. In this light, Stout is careful to specifically carve out some territory within LDT for Christian traditions to participate without compromising the gospel. He states that his project is to "articulate a form of pluralism, one that citizens with strong religious commitments can accept and that welcomes their full participation in public life without fudging on its own premises" (pp. 296-297).
I tend to be critical of Stout in so many ways, but I do think his is an important enough perspective that it requires some engagement.