The Founders used their existing moral philosophies, based in Christianity and other religions, to create the framework of freedom in which the United States is set. The U.S. is not an explicitly Christian nation, but its founding principles came from Christian morals and ideals as interpreted by the Founders. Again, this does not mean that all the documents are Christian in nature, but that their writing -- like most writing of the time -- was inspired by those existing ideals.
The current-day push to remove all religious references, words, and ideas from lawful documents is one that would be alien to the people of the 1700s, simply because people tended to have religious beliefs and so would frame their ideas from that standpoint. In any case, the founding documents should never be censored, nor should any documents. The existence of religious language in the founding documents is a sign of their times, not of religious fundamentalism or oppression. Certainly, the documents have morals based in Judeo-Christian principles, and so do many, many other documents, books, films, and philosophies. Better to examine the substance and the issues at hand rather than focus on the religious influence.