The most adverse effect religion has on US politics is the 'values voters' segment of the population who vote based on issues that are morally out of date as opposed to voting based on facts and broader policy concerns. The right basically gets to use the religious populace as a hate group that will vote for them because they funnel hatred and ignorance to court the votes.
Beyond elections, there is a ridiculous imperative to support Israel based on religious and political backlash potential.