Daniel Dennett and Linda Lascola have published a paper called, "Preachers who are not Believers." The authors extensively interviewed five active preachers who don't believe in God. They are all closeted in this regard. Fascinating reading. Why not just come out of the closet and admit that they no longer believe? You'll see that they believe that they can still do an important job without that core belief. Interestingly, the participants expressed that lack of belief in God is common among active preachers. When asked his opinion of why ministers do not pass on their seminary-learned knowledge of Christian history to parishioners, one of the participants had this to say:

They don’t want to rock the boat. They don’t want to lose donations. They want to keep their jobs. They don’t want to stir up trouble in the congregation. They’ve got enough trouble as it is, keeping things moving along. They don’t want to make people mad at them. They don’t want to lose members. What they will often do is bring in someone like me to be a lightning rod, and teach it, and they’ll follow up on it.

I myself have spoken with at least four active members of the clergy over my lifetime (all of them Catholic priests) who admitted that they don't believe in the God that they describe at the pulpit. They each admitted that this is not an impediment to doing good work as a priest. Dennett's paper parallels his contention (in his book, Breaking the Spell), that most believers don't actually believe in God. Rather, they believe in belief in God. They say they believe because they think it's important to say it, whether or not they actually believe. I have often discussed Daniel Dennett's work at this site (e.g., here). He has a track record of being extraordinarily able to thoroughly think through many topics regarding religion and express his conclusions succinctly.