The idea of separating religion from politics is, in historical terms, a fairly recent phenomenon. The church has been intertwined with the state ever since there was a state (or a church). If the Bible is to be believed, it is impossible to separate the nation of Israel from the worship of the God of Israel.
That doesn't change because the First Amendment exists. Belief in God remains a political asset to be appreciated, expected, and yes, exploited. The left invoked faith to campaign against slavery, the right to campaign against abortion. I would hardly expect TWI to be any different. The Jehovah's Witnesses are rather unique in their resolve to divorce the religion from the politics of this world. The Catholic Church openly embraces political causes, if not parties. Some of the literature I've seen would suggest they care more about opposition to abortion than they do about opposition to the death penalty, but their stances on each of those issues are otherwise equally strong.
I am confident that if you find a church that doesn't try to tell you one way or another how to vote, you have found the exception rather than the rule.