The United States wouldn't have a constitution.
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights..."
It's hard to say where we would be in terms of technology considering many early institutions of academics were affiliated with religion (in order to educate priests/other religious authorities). Early on education was not valued so much outside of religion. Yes, science would no longer be restricted by certain religious teachings, however, the advent of science may have been put off by a couple centuries at least.
Laws would be much more difficult to establish as there were be no consensus on an authority to establish said laws. In particular I believe that foreign relations would suffer as people would be swayed more by cultural values rather than religious values, hence there might be even more prejudice; if this were the case there would also be less spread of technology from one nation to another and likely more wars.
And the list goes on. I am not particularly religious (I am not an atheist but I do not attend church or other religious activities), however, I find the notion that a lack of religion provides one more freedom absolutely ridiculous. When you take God away from people they will not live without a God, they will simply make one of themselves.
How do you breathe again?
