Warin, for an introduction to conservatism in the Burkean tradition, I recommend Conservatism: Dream and Reality by conservative sociologist Robert Nisbet. His chapter “Religion and Morality” outlines the conservative position on religion. He thinks that conservatives stress the necessity of religious institutions for a stable society, but are typically suspicious of religious enthusiasm and are often lukewarm believers at best.
A careful study would undoubtedly reveal that a considerable number of staunch conservatives, disciples to a man of Edmund Burke, had a regard for religion ranging from the indifferent to the outrightly hostile. … Robert Ingersoll, staunch conservative Republican and pillar of bar and bourse, was a militant atheist. H. L. Mencken and Albert Jay Nock … were opponents of Christianity. So was Irving Babbitt and Paul Elmer More, though the latter somewhat unenthusiastically in later years. But all of them would doubtless have agreed with Tocqueville that some bulwark of faith, even if in a body of morality that is falsely credited with divine inspiration, is necessary to human beings and a means of saving them from the worst of the consequences of being among the alienated. (Transaction edition, p. 83)