Christianity Today contrasts the political stances and activities of mainline and evangelical pastors. The data is summed up this way:
[A] new study from Calvin College’s Paul B. Henry Institute shows that for the past decade, evangelical pastors have been more likely to take public stances on political issues and candidates than have their mainline cohorts. Overall, some differences between evangelical and mainline clergy are shrinking as mainline pastors become more conservative and evangelical pastors become more socially active.
This is some interesting data: it suggests both mainline and evangelical congregations don’t hear much about politics even as pastors themselves took stands on particular public issues and a sizable minority supported a political candidate.
On the whole, however, it looks like there are not too many differences here between evangelical and mainline churches in these matters. Outside of more mainline pastors being more liberal on political and economic issues than their congregations, about half of evangelical and mainline pastors engaged in some form of political activity in church. Perhaps we would need some more data to find sharper differences (such as about the particular congregations and contexts where these sorts of activities took place – this could be found in the National Congregations Study) or more qualitative data that could provide insights into how politics is acted upon in particular congregations and through particular pastors.