Tell that to St Thomas Aquinas, whose approach to analytical thinking and the dialectical method approaches Spock-level, if not surpassing it. One might not agree with his conclusions (or even some of his premises), but there's no denying that the man was a rigorous thinker.
Or St Augustine.
Or Professor Einstein.
I would myself assert that people who believe that people who believe in God are not analytical thinkers are themselves not thinking analytically but uncritically regurgitating commonplace bromides produced by amateur intermalekshals who fondly want to believe that merely holding certain opinions automatically either excludes one from consideration as a human being, or else elevates one to unassailable empyrean heights beyond reproach or criticism.
In thinking circles, this is called "being lazily and intolerantly (as well as intolerably) stupid."
or Isaac Newton.