But I think it is a very simplistic way that neglects the history of ideas that surrounds the formation of it,
Actually, in my opinion, to attempt to remove anything related to religion when talking about the DOI or the Costitution is neglecting or ignoring that back then people may have also used their religious beliefs as a guide line to create these documents.
What exactly is commonly meant with "freedeom of religion, not freedom from it"?
My understanding is that as an individual we have the right to believe in any form of religion we chose and no one has the right to take that away from you, but as a group our Gov't can not represent any single religion because of the multiple beliefs found in those the Gov't serves. That is why we are free to believe in any religion we chose not freed from religion. It's not the Gov't or anyone elses job to supress a religion, it is it's job to represent all religions by not representing any in particular.
I don't think I said that they weren't christian or not influenced by it. But the general concept that an individual is born free to do what he wants with his life is not part of official christian doctrine back then.
No, but it is part of life itself, something that those with religious beliefs believe God is responsible for. You have to look at it this way, a religious person will believe that everything has divine intervention in it because it's their belief that God created everything and everyone and therefor God was responsible for the creation of these documents and the freedoms it gives to the US citizens. Why? Because many if not all of those responsible for creating these documents were religious people.
It's as Nitro put it, you can't just turn it on and off when it suits you. Is the aws against taking property that does not belong to you (stealing) a religious concept or non-religious? Interesting to see this is a law that applied everywhere in the US and just happens to be one of the 10 commandments.