Bozell is correct. It is impossible to be both a American Conservative and an atheist.
American Conservatism is about preserving and utilizing the time-honored and proven values, methods, and institutions that have built up America into the exceptionalism that has made it a bastion of freedom.
Insofar as it is in the interest of a free and prosperous people to promote and instill virtue, I do not find it outside the realm of possibility that an atheist could fall into line at least from a sense of self-preservation. But a civil society is much better served when its participants act out of more than self-preservation, seeking the betterment of all. This is partly, if not largely, why we [the citizenry of the USA] argue over the manner and degree of affirming the common good. Pure self-interest is unhealthy and not in accord with the Judeo-Christian ethic that serves our founding principles as expressed and enforceable by law. Most atheists I know seek to question and undermine this very thing, but not all.