Jimmy Carter is a born-again Christian, but he didn't provoke such anger about mixing religion and politics and governing as Bush. Reason -- Carter is Democrat, and it's ok to be a Christian Democrat, but it's not ok to be a Christian Republican. That's why Bush gets so much flack on this issue.
Since Carter, the religious conservatives have been more activist, more aware, more willing to vote their convictions, and their votes have been going overwhelmingly to Republican candidates. Also, since Carter, the so-called "culture war" has heated up so that today it's something of a white-hot battle. This wasn't so much the case during Carter's term. As you suggest, if the vast majority of evangelical Christian votes were going to the Democrats, they wouldn't complain.