Evangelicals share certain values--they can disagree fiercely. To what extent are politicians aware of this?

You're much too sophisticated for the gallery here on Y/A. The trick is that folks like Grover Norquist have run around twisting arms of any and all he feels can be brought to heel for the common cause of electing Republicans. I have heard about the newer generation of clergy that are turning away from the perfunctory backing of the standard GOP candidates. The MSM doesn't do much in the way of differentiating one denomination from the other, so voters are less aware than politicians.