>>Leo Strauss, perhaps the most influential conservative thinker of recent decades, was an atheist<<
I think Russell Kirk had a more important influence on conservative thinking than Leo Strauss. And Kirk was deeply religious.
The attitude we call conservatism is sustained by a body of sentiments, rather than by a system of ideological dogmata. It is almost true that a conservative may be defined as a person who thinks himself such. The conservative movement or body of opinion can accommodate a considerable diversity of views on a good many subjects, there being no Test Act or Thirty-Nine Articles of the conservative creed.