The religious "trust" scale would likely look largely the same. While "deeply religious" may have been the reality for the US at one point, I think it would be hard to argue that with each generation we don't move a little further away from that. As someone who was previously "deeply religious" and am now "non-religious", I still wrestle with whether that's a good thing or not.
The politicization of religion could be argued to be a detriment to the country and also to religion.
The partisan side of politics (as apposed to the policy and persuation sides) has a way of undermining or sidelining the virtues, and the ability to operate with nuance, for any movement that over-identifies with either party.
Virtually any organization can promote a sense of place and belonging in people, facilitate communities, encourage cooperation, etc. Only one type of organization does it by arranging very serious lectures about things that didn't happen.
The average American Protestant doesn't have high trust for religious Muslims, Mormons, Catholics, or even Baptists. Especially a loaded term like "organized religion" in which they see themselves as just a local gathering of Jesus followers, not really "organized" or "religion".