Yes, you are wrong on this particular point, at least, from the point of view of theological principle.
To start with an example, the TEs at BioLogos go to “Bible-focused” churches, but many of them, from their side-comments on social issues, tend to be on the political left.
There is no automatic theological or logical connection between “conservative” or “Biblical” Christianity and Republican voting. There are of course some historical and sociological reasons why those two have become associated in American politics. There is a correlation: in the current culture, the sort of person who is attracted by “conservative” Christianity tends also to be attracted to the political right. But that is not a result of traditional Biblical exegesis or theology; it springs from other cultural factors.
The Democrats actually have themselves (in part) to blame for the strong correlation. Up until about 1972 or so many Christians who were theologically and morally conservative voted for the Democratic Party. Back then, one could be on the “left” on many social and economic issues and still be a very traditional Christian within the Democratic Party, and feel welcome there. Many Catholics, for example, voted Democratic. But sometime in the 1970s the Party seemed to become dominated by intellectuals who were more than merely advocates of redistribution of wealth, and leaned strongly toward secular humanism. So Christians who agreed with things like better medical care for the poor and equal rights for women, but did not agree with other things (e.g., many Catholics regarding abortion) found themselves looking for another party home. And since the small parties play an almost negligible role in electoral politics, their only practical choice for them was to move to the Republicans – even if they were not completely sold on Republican economics. If they felt that they could be very comfortable as Democrats with conservative moral views on many issues, they would have stayed Democrats. Thus, the Republican party became the natural haven of Christian conservatives. If there were a third option, i.e., a party that was left of the Republicans on some economic and other issues, but conservative on many moral and cultural issues, a number of evangelical/conservative Christians would probably support it, rather than the Republicans. This is another case where the crude two-party system in the USA polarizes social and political life. In countries where there are three or four or five major parties, the atmosphere is often less polarized and it’s easier for voters to find a party that aligns more closely with their own views. But Americans have shown very little interest in creating a strong, middle-of-the-road third party.
So obviously, you did not have the experience of UCC or Episcopalian preachers giving sermons that sounded like the lectures of a radical feminist university professor or the program of the left wing of the Democratic Party. You did not have the experience of seeing authority figures in the church, against the wishes of the majority of the worshipers, pushing to changing all “himself” references in sermons, liturgy, etc. to “Godself”. You did not observe the massive exodus of Anglicans from the Episcopalian church over moral and doctrinal issues, to form breakaway Anglican communions. Fine. Our experiences of mainline churches are quite different. But note that the Lutherans, at least the Missouri Synod Lutherans who are more conservative, are not usually examples of what I am calling mainstream liberal Christian churches. Perhaps the other Lutheran groups would be examples of it; I’m not familiar enough with differences among Lutherans to say.
What I’m trying to say is that precisely those churches which have most tried to prove how modern and relevant their Christianity is, by realigning their teaching with current politically correct and secular humanist themes, are the ones whose numbers have been falling pretty steadily for decades now. The only churches that have experienced major growth in the past few decades have been fundamentalist, evangelical or pentecostal ones, the ones who haven’t tried to flatter or imitate the spirit of the age, and have in many cases opposed it.
I agree that individual congregations may differ from the general trend of mainline churches. But overall the big mainline Protestant denominations have de-emphasized classical Christian doctrine and heavily emphasize “updating” Christian faith. Even where they don’t change any formal statements of faith, what is taught from the pulpit, what the ministers says in Bible studies (if the church even has Bible studies – my wife once asked the pastor at a local UCC if they had any Bible studies going, and he looked at her as if she were something from another planet), often contradicts this.