I'm afraid that repeating that US law is not Judeo Christian in origin is simply not true. Modern statistics show that Christianity is still the predominant religion of the USA. The vast majority of the people involved in constructing the Constitution were influenced heavily by the Christian religion, constantly repeating otherwise is flying in the face of fact.

"The country's first two presidents, George Washington and John Adams,
were firm believers in the importance of religion for republican government." --official Library of Congress statement

"...both the legislators and the public considered it appropriate
for the national government to promote a nondenominational, nonpolemical Christianity."--official Library of Congress statement